.lavendar Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈ ⡿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠁⠋⠿⣿⣸⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣿⣿⣿⣿⢿⠙⠀⠀⠀⠟⣿⣿⣿⣿⣿⠻⣘⣋⣙⣁⣛⣭⣧⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡟⣿⣿⣿⣿⣿⣴⣤⣤⣤⣤⣤⣤⣤⣤⣀ ⠀⣄⣷⣿⣿⣿⣿⢿⠻⡿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⠸⣷⣸⡟⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣾⢡⡿⣿⣿⣿⣿⣿⣱⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣉⡉⡟⣿⣿⣿⡈⢃⣿⣿⣿⣿⠛⣛⣛⣙⣉⣉⣉⣉⢛⠟⣿⣿⣿⣿⣿⣿⣱⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⣾⣴⣀⠟⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣾⢀⡀⣦⣶⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ stit eguh htiw 02 mi klim em gnikam meht bur dna stit ym kcus osla i oS sdneirf ym htiw muc em sekam ti radneval. dna yrrebeulb. erom ekam seirots eseht htiw etabrutsam I

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣴⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ashwin⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣷⣔⠂⢦⡀⠀⠀⠀roshan ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⢂⢹⣿⡷⡄⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡄⠙⠻⠿⠿⠛⠁⠀⢩⠯⣝⠗⠡⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣦⡀⠀⢘⡂⠚⠡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠐⢱⠄⠀⠅⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⡧⠘⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠇⣾⠀⠀⠀⠀⠀⠀⠋⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⠀⡇⢰⠀⠀⠀⠀⠉⠟⣶⣴⣤⣤⣤⠤⠷⠿⠲⠓⠉⡏⠀⠀⠀ ⠀⠀⡇⠀⠀⠋⠖⣤⣀⠈⠀⠀⠀⠀⠀⠀⠀⣦⠘⠀⠀⡁⠀⠀⠀ ⠀⠀⡆⠛⡴⢀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢧⠈⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀ ⠀⠀⠀⠀⢦⠈⠀⠀⠀⠄⠈⠀⠀⠃⠐⠀⠀⠀⠀⠃⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠑⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠰⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠈⢆⠀⠀⡇⠀⠀⠀⡜⠀⠀⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠊⡠⣀⣀⣤⠳⢎⠀⡄⠀⠁⠒⠒⠶⡿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠃⢖⠶⠲⠛⠉⠉⢆⠀⠁⡔⢉⠋⠛⠛⠉⣆⢻⠀⠀ ⠀⠀⠀⠀⠀⣴⠀⠀⠀⡀⣀⣥⣭⣭⣬⣓⢛⠒⡐⣀⣤⣶⣶⠸⠀ ⠀⠀⠀⠀⠇⢶⠙⠀⠀⠂⠴⠐⠂⠒⠑⠉⠉⠈⠀⠀⠀⠀⠁⢸⠀ ⠀⠀⠀⠀⡄⢹⡀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠔⡯⣶⠘⠀ ⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠉⠀⠀⡁⣉⢈⠤⠤⠠⠀⠀⠃⢸⠀ ⠀⠀⠀⠇⢠⠀⠀⠀⠀⠁⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠉⡶⠒⠀⠀⠀⠤⡠⣀⣀⣀⣀⠤⠤⠠⠀⠀⠤⠀⠀⠧⣸⠀ ⠁⡿⢛⠉⠀⠀⠤⠠⠂⠒⠓⠛⠚⠒⠀⠒⠐⠀⠀⠀⠀⠀⡇⢠⠀ ⠎⣾⣤⢝⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠀⡀⠘⠀ ⣦⢼⠀⡀⢦⣷⠙⠍⠢⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⣄⢓⠈⢃⠀ ⠀⠄⠂⠗⠉⠀⠀⣀⣄⣤⣤⣤⣦⣶⣶⣶⣈⣀⢤⠤⠛⠃⡍⣼⢻ ⠀⠀⠀⠸⡀⣄⠶⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣜⣆⣿⣽⣰ ⠀⠀⠀⢇⠀⠀⠀⠀⠀⣀⣀⠤⠢⠒⠓⠙⠉⠉⡏⣰⠀⠏⣾⢀⠀ ⠀⠀⠀⡀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⣠⣂⠒⠔⣠⠀⠀⠀

⠃⠛⠛⠛⠿⠿⠻⠀⠀⠀⠀⠀⠇⠿⠿⠿⠟⠿⠿⠿⠿⠿⠻⠙ ⠀⣀⣀⣀⣇⣿⣽⠛⠉⠀⠀⠀⡇⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣴ ⠀⠀⠀⠀⡇⣿⣿⣿⣿⠻⠛⠙⡟⣿⣿⢸⣇⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⢻⡇⣿⣿⢿⠀⠀⠀⠀ ⠀⠋⡿⣿⣿⣿⣿⢀⠀⢀⣷⢿⣝⣷⣿⣴⡏⣿⣿⣿⠘⠀⠀⠀ ⠀⣷⣿⣿⣿⣿⣸⠀⠀⠀⠀⣦⣿⢻⠈⠃⣿⣿⣿⣿⢰⠀⠀⠀ ⠀⡀⣤⣶⣴⣠⠀⠀⠀⠀⠀⠀⣆⣿⣿⡿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣶⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢹⠄⡀⢀⠀⠀⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⠰⢉⡧⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡑⢂⡱⡜⢿⡀⠀⠀⠀⠐⠀ ⣿⠘⠤⣲⣰⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⡘⠆⠃⣇⣿⢺⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⡌⠡⡼⣏⠸⣠⣄⢈⠀⠀ ⣿⢿⠀⢀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠃⢀⢩⡧⣿⢻⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡈⢱⡖⡍⢻⢀⠀⠀⠀⠀ ⣽⣿⠸⠐⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠤⢋⡧⣿⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⡃⠤⢚⣯⠘⠀⠀⠀⠀ ⣾⣟⢻⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡰⠜⡯⣟⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠘⣩⠖⣍⢻⠀⠀⠀⠀ ⣽⢾⣿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⡨⠖⣏⡃⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⡃⠤⢚⣯⠈⠀⠀⠀ ⣻⣽⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡒⢎⣏⡇⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠒⣎⠇⣎⢹⠀⠀⠀ ⢾⣳⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠴⢛⣯⡁⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⠰⢍⢢⡜⣿⠀⠀⠀ ⣟⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⡱⢎⣿⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠕⣊⠭⣗⠸⠀⠀ ⢻⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣁⡓⢧⢸⠔⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠣⢆⡙⡧⢸⠀⠀ ⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠥⡂⡱⣾⠀⠀⡦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⢢⡜⡎⢽⠀⠀ ⡽⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠜⠃⣡⡿⢻⠟⠹⠋⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡉⠦⢃⢰⣾⠀⠀ ⡷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢂⡁⠆⠡⣿⣤⣀⣷⣿⣿⣤⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡱⢆⡡⢽⠀⠀ ⣷⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢡⠠⡘⠣⣾⢀⠀⠀⡉⣿⢬⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡰⢓⢡⡷⠀⠀ ⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠂⡁⠟⣾⢀⠀⠀⠀⡀⣿⡐⠀⠀⠀⠀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠡⡱⠢⣑⡷⠈⠀ ⡿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠏⡴⢆⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡡⠒⣡⡜⡯⠀⠀ ⡷⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡾⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⣦⠙⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠒⠌⣃⠠⢳⡌⣟⠀⠀ ⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢈⢠⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⣄⠹⠀⠀⠀⠀⠀⡘⠁⠄⡃⠄⡑⠢⣌⠚⢡⣾⠀⠀ ⡵⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠂⡀⢶⠈⠀⠀⠠⠄⠂⡐⠎⡁⠰⢎⡃⡔⢏⢸⠀⠀ ⣳⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⢂⠁⣆⠑⠀⡐⠎⢁⡰⠎⢃⡄⠘⢱⡬⡟⢀⠀⠀ ⡾⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠌⠂⠁⠠⡐⡌⠆⡈⠱⢌⠡⠴⡈⠴⡓⣸⠀⠀⠀ ⣟⢧⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⠀⡐⠂⢁⢢⡐⠱⡌⠆⡈⠖⣈⡿⢀⠀⠀⠀ ⡼⢿⣯⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⡐⠌⠁⠤⡈⠢⡐⢌⡑⠦⢏⣰⠀⠀⠀⠀ ⣽⡞⣿⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠌⠂⠄⠈⢂⠔⢂⡡⠟⣼⠀⠀⠀⠀⠀ ⡳⣽⣸⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⢂⠄⢈⡐⢋⡷⣼⠀⠀⠀⠀⠀⠀ ⣼⡟⢰⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⢡⡀⠞⣫⣼⠀⠀⠀⠀⠀⠀⠀ ⣜⡿⢀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠐⠁⡼⢏⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⢰⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠃⢥⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢠⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡱⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⠈⠀⠀⠀⠀⠀⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠋⡷⣎⡞⢿⠈⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢑⡦⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠟⣾⣡⣸⢍⠂⣄⢻⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢨⠱⢂⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⡇⣩⠴⢋⠤⠒⣈⠑⣇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⠆⡉⠤⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢃⢆⠡⢶⠻⢉⠠⡐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠉⢢⡜⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢈⡱⢂⠤⡘⣆⢿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⢋⢠⢽⡎⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠈⡰⠁⢂⠄⠩⣄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠇⣡⠖⢩⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⢸⠌⡀⠀⠀⠀⠐⠠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢾⡉⡰⢜⡻⣇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⢸⠀⠀⠀⠀⠀⡁⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢿⠠⡱⢆⠳⣇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠂⠀⣿⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⢊⠀⣿⣉⠤⣣⡕⡪⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠁⣼⠁⠉⠛⠛⠛⠿⠿⠛⠛⠉⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠋⠟⡿⣾⣛⣳⠾⣟⢿⢯⣿⠓⣘⡕⢻⢰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢀⠀⠀⠀⠁⠔⢔⣠⠀⣠⣀⠀⢀⠀⢀⡀⣀⣄⢦⣷⢽⠻⠙⠈⠀⢸⠀⠀⠁⠛⡿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡥⣬⡷⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠏⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡶⣟⢯⠙⠋⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡧⣿⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠁⣸⠀⠀⡿⣯⣿⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢿⣋⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠵⣿⣟⠻⠙⡀⣷⡋⢤⠀⠀⠀⠀ ⠀⠀⠀⡇⡯⢀⠀⠀⣿⣿⡧⣿⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣟⣯⣏⠿⣯⠀⡂⣿⢀⠀⠀⠀⠀ ⠞⡿⢤⡿⡎⠀⠀⠀⣄⡤⣶⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡶⣻⣺⣴⢀⠀⠀⣗⢹⠦⠷⠹⠀ ⡟⢠⠁⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡎⣜⠀⡃⣿⠀ ⣧⠈⡇⣿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡬⢩⠟⣿⢰⠀ ⠁⢄⠟⣹⣇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣉⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢣⣕⢻⡴⢠⠀⠀ ⠀⠢⡀⢸⠀⡄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠅⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡗⣠⠐⢊⡱⣷⠀⠀⠀⠀ ⠀⠀⣇⢸⠀⠀⠀⠀⣄⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⡀⠀⠀⠀⡀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠝⣑⣠⠀⠀⠀⠐⣈⡷⠘⠀⠀⠀ ⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⡀⣷⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣽⣄⢀⠀⠀⠀⠀⠀⡐⡇⢸⠀⠀⠀ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⠀⡐⢂⢿⠙⠀⠀ ⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢨⠀⠀⠀⠀⠀⠀⠀⢁⢸⣀⢳⠀ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⢧ ⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡾⠀⠀⠀⡀ ⠀⠀⠀⠀⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢙⠀⠀⠀⠀ ⠀⠈⠀⠇⣱⢾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠘⠀⠑⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢆⠘⠀⠀⠀⠀⠀⠉⠟⣾⣻⣧⠹⠀⠀⠀ ⡰⠀⠀⡇⡀⢸⡇⢌⠻⠛⠉⠉⠁⠄⠈⠀⠀⠀⠃⠒⠒⠞⠤⡿⣠⣀⣀⢁⠋⢠⠀⠀⣃⢀⠀⣇⣸⣄⣦⣒⣝⢬⠶⠒⠀⠀⠉⠉⠋⠟⡿⣇⣽⣿⣷⢲⣿⠘⠀⠀ ⠀⠀⠀⡇⠘⢹⡏⠰⣇⢾⢹⡀⣆⣿⣿⣇⣿⢿⠻⠙⠈⠀⠃⣼⠀⠀⠀⡏⣰⠀⠀⠀⡄⠸⠂⡀⢿⠘⠂⠍⠒⠤⣠⣀⣄⠘⢀⠀⣿⣿⣿⠀⡡⣿⡇⣼⡿⣿⠀⡏ ⠀⠀⠀⠀⢳⣇⣿⠰⡇⢸⣻⠀⠀⣇⣿⠈⣿⣷⣿⣿⣾⢧⡿⢘⠀⠀⠀⣰⠀⠀⠀⠀⠀⢧⠁⠄⣿⢴⣠⢀⠀⠀⠀⠀⡇⢿⠀⡇⢽⣰⣿⠀⠀⣿⡇⣼⡟⣿⠿⣸ ⠀⠀⠀⠃⡷⠘⣷⢹⡀⢠⣿⠀⠀⡀⣾⣧⣇⡀⣿⣿⢿⣏⢠⣇⠀⠀⠀⠀⠀⠁⠜⠀⠁⡏⠰⡯⢀⠀⠀⠀⠀⠀⠀⠃⣾⣀⠁⣼⠀⠇⣸⠀⠀⣿⡇⣸⣿⣯⣼⠀ ⢳⠈⠀⣸⡇⢿⡌⣧⠘⠀⣆⡌⠘⠀⢸⡇⡼⠀⣿⣿⣿⣸⠀⡇⠀⠀⠀⠀⠏⣾⣫⠷⠹⣈⠐⣿⠀⠀⠀⠀⠀⠀⠋⣿⢀⠃⣾⠄⠁⡞⠀⠀⡇⣸⣄⡏⣼⣿⠙⠀ ⠂⢟⠟⢿⡆⡽⢻⡄⣷⠸⠀⢀⢸⠀⢸⡇⣸⠁⣿⢳⣾⠀⠀⡇⠘⠈⠋⡿⣼⣞⢯⣳⣽⢿⣋⣿⠀⠀⠀⠀⠀⠏⣯⢠⠃⡼⢨⠁⡿⢠⠀⠀⡿⢀⠃⣾⠏⣰⣿⠸ ⠀⡎⣻⣬⠳⣌⣳⢿⡈⢳⠘⠀⢿⠀⢠⡿⠡⡟⣣⣿⢠⠀⠀⡇⠿⣿⣿⣿⣶⣴⣤⣷⡿⣿⣿⣿⠀⠤⠀⠈⠇⣸⣸⠁⣼⣇⠀⡟⣰⠀⠀⠏⣰⠁⡾⢥⡼⠁⢹⢸ ⠏⣭⢞⣭⠶⣟⠻⣍⢶⠙⡀⢤⡉⢨⠇⣻⡟⢿⣯⣼⠀⠁⠋⡶⣤⣠⢀⠀⠀⠀⠀⠀⡀⣦⣷⣿⠀⠀⠀⠀⡧⣀⢹⡏⣂⡙⠀⣼⠀⠀⠏⣰⠃⡵⠟⣾⢀⡞⡟⢀ ⢾⣍⠽⣣⣜⠳⣌⣇⣤⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠟⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢳⠈⠀⠀⡀⢹⡆⢹⠀⠄⠂⢁⠠⠟⣰⠀⢋⡿⣴⠋⡵⡞⢀⢸ ⢞⢣⡹⢧⡌⠳⣀⠰⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣽⠛⠘⠁⠘⠈⠀⠀⠛⠞⠤⠠⠒⠑⠈⠀⠀⠀⠀⣤⠛⠉⠀⡀⢻⣿⠙⠀⠀⠻⡷⣠⠋⡽⣾⣩⠿⢞⣠⠁⡟⢠ ⡜⢮⡙⢢⡜⠣⣀⠀⠋⡿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣞⢵⣸⠵⠀⠀⠀⠀⣀⣀⠄⠤⠤⣤⠠⠏⣟⢆⣉⡀⣷⢿⠿⣿⣿⣿⣿⢿⠻⠿⣿⣿⣿⣾⣴⣠⠉⠟⣴⢀⠀ ⡖⢌⡱⢎⡌⠀⠃⡿⣿⣿⣿⢧⡟⣿⣵⣟⢿⣿⣰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣖⣆⣇⣏⢛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⠶⡴⣤⣀⠀⠀⠀⠀ ⢣⣌⡓⠌⢀⠀⣿⣧⣾⢠⣾⡟⣿⣰⡰⡟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⢀⢧⠀⠀⠀⠀⠀⠀⡀⣄⠳⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡌⠒⢀⠀⡇⣼⡟⢠⡁⢿⣽⣾⡀⠇⣿⢁⠈⠀⣋⣛⣛⠤⠀⠀⠀⠀⢤⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣻⢿⣿⣿⣿⣿⡿⣿⣿⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡜⠀⠀⠀⡇⢸⣟⠀⣿⣾⣇⢨⠀⣧⣿⣿⠸⡍⣯⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠏⠭⠤⠑⠀⠀⣷⡸⣖⣿⣿⣿⢧⣿⣿⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡜⠈⠑⠢⡇⣽⣿⠀⣿⢠⡄⠀⠠⡿⣿⣤⣿⣿⣿⣿⡿⣾⣷⠻⠙⠙⠀⠀⠀⠀⠁⠋⡶⣾⣿⢿⠈⢧⠈⡇⣿⠄⣇⣿⣿⡔⣿⣿⡧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⡀⡄⠀⢠⡄⣿⣷⠀⣽⠀⡀⠀⠃⣿⢠⠀⣿⣀⣄⣿⣿⠈⡇⣄⣷⣿⢽⠢⠎⠈⡄⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⢘⡡⣿⣿⡚⣷⢸⡿⢸⠈⠠⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⡟⠈⢹⠀⠀⠀⡇⣼⠀⠀⡇⢸⠀⢹⡄⣷⡟⢻⠉⣧⣿⢻⣯⣿⠈⡀⣿⣬⣾⣷⣹⣇⣹⡆⣿⢾⠈⣿⣿⡐⣾⠇⣿⢀⠀⠁⠂⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⠀⠀⠰⡇⢺⠙⠈⣤⣻⣈⣾⣶⣽⣦⣿⣦⡻⣤⣿⣿⡆⢹⠀⣇⢿⢸⡀⣯⣿⢢⠀⣷⢿⠀⣏⣼⡏⢣⣿⢠⠄⠀⠈⠀⠐⠀⠀⠈⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⠸⠀⠀⡇⢈⠀⣀⠦⣷⢿⢸⠀⡀⢷⡈⢤⣇⠸⣷⣿⠀⣯⠀⡿⣿⠀⠀⣟⣿⠀⢁⡤⣹⢀⡿⢃⣿⣾⢨⡀⠁⠀⠀⠐⠀⠂⠄⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣳⣿⠀⠀⡆⠘⠀⠀⠀⡆⣿⣟⠸⠀⡇⢦⠘⠀⣷⠃⣸⠀⣟⠋⣿⢻⠛⠓⣿⢾⡤⠀⠇⢸⠏⣱⣿⣾⢁⠀⠂⠀⠀⠠⠀⠈⢀⠁⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣀⢱⠀⠀⢸⠀⠀⠀⡇⣷⢸⣇⠈⡃⠀⢧⠀⣇⠃⢰⣀⣿⣿⣾⠀⠀⡞⣏⢀⠃⢀⡞⠃⣻⡿⣴⠀⠀⠂⠀⠀⢀⠀⠠⠀⠂⠀⠀⠐⠄ ⠀⠀⠀⠀⠀⠀⠉⠛⡴⣀⢳⡀⠱⠀⡇⠀⠀⠀⡄⡼⢸⠀⢳⠀⠀⡇⢸⡇⡄⠀⠇⣿⣾⢀⠀⡞⣏⣸⠃⢰⠖⢫⣽⡿⢠⠀⠠⢀⠀⠂⠄⡀⠀⠈⢀⠂⠀⡀⠀⠄ ⠒⠒⠄⠤⣤⣠⣀⠁⠀⠀⡀⠳⡈⢤⠑⢠⠃⠀⠀⢣⢸⠀⡇⠈⠀⡼⠀⣼⠀⡅⡾⣿⠀⠀⡀⠟⣼⠃⣠⡁⠏⣿⡼⢀⡀⠀⠈⠠⢀⠀⠂⠄⠀⠀⠄⠀⠈⢀⠂⡀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢆⠑⡀⠠⠈⢣⠀⡄⢸⠀⠀⢸⠃⢠⡇⢀⠁⡴⢁⠠⠀⠃⡿⣰⠀⠀⠟⡿⣾⣠⠁⡀⠀⠐⠀⠁⠄⡀⠀⠁⠄⡀⠀⠐⠀⠄⠀⡁ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⡀⢤⠓⠈⠀⢄⠑⡄⠑⠀⢠⠀⠃⢡⠞⣠⠜⢀⠁⠞⣴⢀⠀⠋⡿⣴⣠⠄⡀⠀⠀⠠⠀⠀⠠⠀⠂⡀⠀⠀⠐⠠⠀⠠⡀⠀⠐ ⠀⠀⠄⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⠀⠂⠀⣀⢤⠒⠙⢈⡀⠠⠐⠁⢋⣤⠀⡠⠀⠀⣠⠁⠉⠛⠶⣤⢀⠈⢀⠀⠐⡀⠀⠀⠠⢀⠁⠄⠀⠈⢀⠁⠂⠀⠠⠀⢀⠈⠄ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⢤⠿⠬⠶⡶⢶⠶⠴⣤⣤⣠⣄⠀⠀⠂⠀⠀⠀⠠⠀⠈⢀⠀⠄⠀⠈⠁⠀⠈⠁⠀⠈⠄⠀⢀⠈⠁⠀ ⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠄⠀⠀⠄⠀⠀⠠⠀⠄⠀⠀⠐⠠⠀⠐⠀⠂⡀⠀⠐⠀⠐⠀⠈⠐⠀⠈⠐⡀⠁⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠛⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⠻⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⠐ ⡏⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣾⣴⣀⣀⣀⣀⣀⣀⠀ ⡆⣿⣿⣿⣾⠀⡀⣦⣿⣿⣿⣀⣁⣋⣞⣿⣿⣿⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣀⣀⠀⠀⠀⠀⣇⣿⢿⡿⣿⣿⢿⣯⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠋⠙⠈⣷⣿⣿⣿⣿⣴⢣⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣿⣿⣿⣿⡸⣤⣤⣠⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠠⠐⠁⠉⠛⠿⢟⡽⣊⠤⣀⠀⠀⣀⠀⠀⠀⡀⢆⠈⣿⠘⣇⡑⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⡀⣿ ⠉⠉⠏⡿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⡇⢻⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠀⠋⠀⣇ ⡀⣧⣿⣿⣿⣿⣿⣼⠀⠀⠇⣠⣆⠀⠀⠀⠉⠋⠉⠉⠟⣿⣼⢀⠂⢽⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⢡⠀⠋⡾⢸⠁⡟ ⠋⣿⣿⣿⣿⣿⣿⠉⡉⣏⡸⠹⠀⠋⠿⣾⣿⣿⣿⣿⣾⣹⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡠⠀⠄⠃⡿⣭⣿⢿⢿⣿ ⣿⣿⣿⣿⣿⣿⣱⣋⢟⣿⣿⣻⡿⣿⣠⠟⣿⣿⣿⣻⠿⡿⢿⠙⡟⢨⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠡⣖⢌⠐⢣⠛⣿⣿⣿⣿⣿⢰⣿⣿ ⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣅⣿⣿⢀⡟⣿⣿⣿⣿⢛⠘⡀⣿⣿⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⠒⡤⣁⢋⠟⡿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡿ ⣯⣿⣿⣿⣿⣿⣿⣡⣼⢀⡿⣿⣿⡟⣿⣿⣿⣹⠉⡇⢻⡿⣿⢻⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠉⠖⡹⢫⠛⠟⡿⣿⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⣿⣿⣿⢸⡿⠀⡇⣿⣿⣿⣿⣿⣿⣰⠀⣏⡿⣿⣿⣿⠱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⠙⠛⡿⣼⣏⣿⣿⣿⣯⣿⣾⣾⠙⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇ ⣿⣿⣿⣿⣿⣿⢿⣿⠀⡿⣿⣿⣿⣿⣿⣸⠀⠏⣿⣿⢻⡿⣨⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣼⣞⡇⠂⣀⣀⣤⣥⣿⣦⣿⣧⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣹⢎⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠀⠀⠁⠈⠉⠉⠈⠀⠀⣧⣿⣿⣇⣿⣿⣿⣿⣿⢃⢷⣣⢜⢩⠠⠀⠀⠀⠀⡀⢄⣶⣿⣿⣿⣿⣿ ⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣿⣨⣿⣿⢦⡙⠦⣊⠐⠈⠀⠀⠀⠀⠈⠁⠂⡀⠑⠌⠊⢣⠆⢋⢓⠶⣬⣤⣠⣄⣀⣀⣀⣤⢤⠶⣷⢠⡿⣿⣿⣿⣿⣿⣳⣹⢦⡜⠒⢈⠀⠀⠀⠀⠀⠀⠀⢤⣇⣿⣿⣿ ⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡅⣿⠿⣿⢲⣝⠣⢦⠔⢫⠔⠊⠁⠃⠄⠙⢢⡱⢆⡩⠜⢫⢽⣦⣈⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣦⣿⣿⣿⢡⣻⢦⡙⢦⡙⢦⡈⠐⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⣾⣾⣷⣬⣹⣦⣵⣮⠿⡹⢞⡡⠜⡪⠕⣣⡙⢧⢏⡷⢤⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣷⣿⣿⢞⣡⠜⢣⡄⢻⢄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿ ⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣬⡜⢂⢠⡄⠀⣀⠠⢄⠡⡰⣯⢷⡩⢞⡡⠶⡙⢾⣹⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣹⠜⢣⠡⢠⠀⡄⢳⡈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠁⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣌⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⣦⠿⣩⡼⡟⢼⡑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢺⡕⢃⠠⠀⠀⠀⠀⣄⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⡇⣿⣾⢀⠀⣄⣷⣿⣿⣺⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡃⢦⡝⣽⡘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠑⢀⠀⠀⠀⠀⠀⠀⣯⠿⠙⠈⠀⠀⠀⠂⡀⢇ ⠀⠀⣿⣾⢀⠀⠀⠀⡇⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡁⢬⡹⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁⠠⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢿⠙⠀⠀⠀⠀⡏ ⠀⠀⡷⢸⠀⠀⠀⠀⡇⣼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡔⡝⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠗⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣻⣷⢿⠻⠏⡟⢿ ⠀⠀⡆⣌⠐⠀⠀⠀⠀⢸⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡌⡚⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣲⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣻⣿⢾⣤⣀⣀⣦ ⠀⠀⠀⢆⡘⠡⠀⠀⠀⢣⠁⡛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠌⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠘⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⢾⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠳⢌⠉⠀⡀⣧⡘⣦⡖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡝⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⢰⠀⠁⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣇⣿⣿⣿⢣⠙⠉⠋⡸ ⠀⠀⠀⠀⠀⠀⣄⡷⠻⠀⡀⣷⢿⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⠘⠀⡿⣸⠐⠀⠀⠀⠀⠀⠀⠋⡴⣿⣿⣿⡿⣿⣿⢿⣿⣯⡷⣟⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠳⠙⣿⠻⡀⢄⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡾⣠⠜⢀⠖⣾⡔⠈⠀⠁⠋⠛⠾⣤⢀⠇⣿⣿⣿⣿⣿⣿⣿⣾⣟⣾⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⢻⠈⡆⣿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⢶⣁⠐⠀⠇⢾⣉⠟⣿⣾⣤⣀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣴⣟⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠁⠛⠛⠒⠀⠀⠀⠀⡀⣷⣿⣿⢿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠁⠉⠛⠟⣿⣿⣿⣿⢊⠄⢀⠀⠀⡟⢿⣶⣠⢀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣼⠏⣷⣿⢀⠀⠁⠚ ⠀⠀⠀⡿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡿⣾⣿⣾⣏⣿⣠⠀⠁⠊⠟⡿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⣿⣿⢋⣿⣿⣰⠀⠞⣣⢡ ⠀⠀⠇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣷⣿⣿⣿⣿⢻⣷⣾⣝⣧⣾⣽⣦⣿⣿⣻⠆⠘⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⠀⣿⢿⠀⠇⣹⠟⣿⣼⡀⣄⢿⠈⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣾⢠⠃⡴⡕⢪⡰ ⠀⠀⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣾⡿⠦⣈⡖⢹⡄⢻⡈⣷⣿⣿⢰⠁⠂⠁⢀⠌⠂⠁⠀⣷⣿⣾⢿⣿⣿⢻⣇⣿⣿⣿⢠⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⠛⡾⢀⠒⠉⠀⠀ ⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢺⡅⣿⣿⣶⣍⠢⢄⡀⠀⣇⠰⡆⢿⡎⣿⣽⢈⡱⠆⢉⡰⠌⢃⠐⠳⡘⣬⣷⡙⣤⣷⣿⣿⣿⣿⣿⠂⠈⠀⠀⡄⠸⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⣟⣿⣾⢀⠀⠀⠀⢏⠟ ⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢽⡏⣼⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢺⡔⡙⠤⢛⡾⣕⢊⡰⢓⣌⢶⠶⡾⣷⣿⠿⣿⣿⣿⣿⠸⡀⢢⠁⠀⣏⠙⠀⠀⠀⠀⡟⣿⣿⢷⣿⣿⣼⢀⠀⠁⠟⣵⣿⣴ ⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⣏⣿⣿⢶⣋⠞⣻⣧⡌⠲⢏⡷⠛⡄⡜⠣⢌⠲⠍⣛⣮⣷⣿⣿⣿⠛⢉⠛⡸⠀⣄⢿⠉⠉⡟⣿⣿⣾⣿⡿⣽⠻⠁⠟⣴⢋⣾⢀⠀ ⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠎⢣⣟⣿⣿⣷⣛⣆⠜⢪⡴⢙⣦⢛⣄⢺⡜⠳⢎⢡⡴⠎⣇⣯⣿⣿⣿⣿⣿⣿⠿⠿⠻⡿⣿⣿⣿⣿⣿⣯⣽⡾⣧⡾⣽⢃⡾⣠⠀⠁⡗ ⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠁⡟⢦⢀⠀⠀⠋⠾⠶⠒⠈⠀⠃⡿⢮⣙⢿⣿⣿⣿⡿⣿⣼⠿⣏⣚⠗⣈⡿⢼⡒⠜⠣⣆⣻⡜⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣟⢰⠀⣿⣿⣼⢀⠀⠞⣻⣰ ⠀⠀⠀⠀⠀⠆⠘⠀⠀⠀⠀⠋⣳⡰⢀⠀⠀⠞⣠⠀⠀⠀⣆⠈⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⢽⢻⡿⣿⣴⠏⣁⠲⢎⣃⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⠀⡟⡾⢾⢸⠋⡳⣾⢠⠀ ⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠟⣬⡰⠀⠀⠀⡜⠀⠁⠟⣾⢶⠓⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣾⣱⣏⠖⣠⣀⣄⢤⡲⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⢾⢸⠏⣼⢀⣇⣷⣟⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢿⠀⡞⢳⣀⠀⠀⠀⡄⠀⠏⣴⢀⠀⠋⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣵⢏⡼⢀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣾⡿⣞⣿⣼⠀⠀⡞⣟⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡾⣜⠠⠀⠀⠀⠀⠀⠏⢠⠀⠀⠏⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣠⠀⠀⠀⡀⣤⣠⣤⠀⠀⠄⣀⣀⢎⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣾⢀⠀⠟⣾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣹⢀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠇⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⠚⠤⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡀⣁⢡⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⡿⢰⠀⠏⣾⢀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣼⠐⠀⠀⠀⠀⠀⠁⣸⠀⠀⠋⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣰⢀⠀⠀⡀⢆⠻⠌⠙⣤⠀⠀⠀⠁⠋⡒⠉⣬⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⠀⠁⣿⢀⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⣘⠀⠀⠀⠀⠀⠀⡇⢠⠀⠟⣿⣿⠃⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⠂⠀⠐⠀⠀⡂⣷⣿⡻⢟⠙⠀⠗⣼⣫⢾⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⡟⢸⠁⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡴⠈⠀⠀⠀⠀⠁⠁⣼⠀⡞⣇⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣚⠡⣉⡙⠉⠉⢄⡸⣿⣿⣿⣿⢿⡹⣶⣿⣿⣿⣿⣼⣧⣧⣿⣿⣿⣿⡷⣿⣿⡏⣾⠀⡿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣺⢌⠀⠀⠀⠀⠀⠰⡟⢸⠃⢠⡏⣿⣷⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠟⣾⣩⣚⠗⠉⠏⣽⣿⣿⣿⣿⣿⣿⢿⣛⣦⣿⣿⣿⣿⣞⣿⣿⣿⣷⣯⣿⢾⣿⢰⡟⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢒⢈⠀⠀⠀⠀⠀⢃⣿⢀⡇⣭⣢⢍⢣⡿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢯⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣿⣿⣏⣿⣿⣯⣿⣿⣿⣽⡟⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡽⠎⠀⠀⠀⠀⠀⠀⡟⣸⠀⣾⠃⢆⢋⣿⣧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⢿⣾⣻⣿⢿⣯⣿⣿⣽⣻⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢾⠃⢀⠀⠀⠀⠀⠁⣿⢸⡞⣀⠘⢣⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣈⣿⣿⣿⣳⣿⣿⣟⣿⣯⣿⣿⣿⣯⣿⣯⣟⣿⢿⣯⣿⣿⣻⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠼⢨⠱⠀⠀⠀⠀⡏⣿⢰⠀⢌⠃⣿⣿⣿⣿⣴⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣷⣿⣯⣱⢾⣯⡵⣿⢾⣟⣿⣽⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⣻⢌⠣⠀⠀⠀⠇⣿⣼⠉⡔⠋⣿⣯⣿⣽⢋⡾⣴⣠⢀⡄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡿⣶⣫⣵⣟⢺⣹⣿⣏⣻⣼⡟⣿⣾⣝⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢻⣌⠐⠉⠛⠟⢿⣿⢹⠛⠿⣻⠿⣶⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣞⣿⣿⣽⢾⣻⣷⢟⣯⡽⣾⣛⢿⣽⡾⣟⣿⣻⣗⢯⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣄⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⡽⣿⣿⣿⣿⣽⣻⣷⣟⣯⡷⢯⣳⣽⢾⣿⡯⣿⣿⣞⡳⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⣿⣿⣿⣿⣏⣿⣿⣽⣿⣿⡾⣟⣿⢾⣿⣿⣿⣾⣟⣯⡷⣟⣳⣟⣳⡾⣟⢾⣿⢯⣿⣏⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠘⠂⠀⠀⠀⠀⠀⠁⠀⠊⠁⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⣿⣤⣷⣿⣿⣿⢿⣯⡾⣟⣿⣿⢾⣿⣯⣿⣿⣟⢯⣳⣽⡽⣾⡽⣻⣵⢾⣟⢯⣽⢯⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢌⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣵⣀⢀⠈⡁⣬⣷⣾⣶⣿⣻⣿⣿⣿⣿⢿⣿⣿⣿⣟⣻⡿⣟⢯⣽⠿⣯⣝⡿⣯⡟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣿⣿⣿⣿⣿⣴⢫⠶⡉⠖⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠟⣿⣿⣿⣿⣿⣸⠈⡉⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣽⣴⢟⣾⢫⡵⡉⡂⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⣿⣿⣾⣶⣷⣿⣿⢿⡙⣶⠻⣮⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣸⢯⣿⣽⠿⠗⣥⣁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣶⠒⠐⠆⠶⠶⠛⣛⠩⣄⢷⡙⣧⣿⣿⣶⣿⣿ ⣿⣿⣷⢰⣿⣷⣿⡿⣴⣋⡿⣿⣿⢻⣛⣝⣤⣷⣿⣿⣿⣿⢠⣥⣭⢿⠙⠈⣀⣛⠉⠤⡲⣛⣉⡏⣿⠹⣧⣴⠀⠋⣿ ⣿⣿⣿⢨⣿⣟⡿⣠⡟⣿⣿⣿⣿⣿⣿⣿⣿⠻⣜⣴⣋⠟⡿⣿⣿⣿⣿⣿⢿⡻⣉⣬⣶⠿⣿⣿⣿⣿⠻⡆⢸⡿⣿ ⣿⣿⢷⢰⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢡⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙⣦⣿⣿⣿⣿⢻⠈⣿⣿ ⣿⣿⣯⢸⡿⣿⢐⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣿⣿⣿⣿⢻⡌⣿ ⣿⣿⣿⢸⣿⢲⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣿⣿⣿⣿⢿⣆ ⣿⡿⣿⢸⣷⢼⠐⣷⣿⣿⣿⣿⣿⣿⣿⣼⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⣮⣿⣿⣿⣼⠁ ⣿⣿⣻⢸⣿⣿⢀⡏⣿⣿⣿⣿⣿⣿⣼⢸⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢃⡿⠿⠌⠁⣬⠋⣿ ⣿⣿⣿⢸⣷⣿⢃⡄⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢁⣿⣿⣿⣿⣿⢁⣿⣿ ⣿⣿⣿⢹⡇⣿⢻⢸⣇⣿⣿⣿⣿⣿⣿⣾⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢃⣿⣿⣿⣿⣿⢰⡟⣿⣿ ⣟⣿⣿⣿⡂⣿⣿⢿⠀⣧⣿⣿⣿⣿⣾⢀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢁⣿⣿⣿⣿⣿⣼⠏⣿⣿⣿ ⣿⣿⣿⣟⢈⣻⣿⣿⠊⠓⣆⣿⣿⣧⢀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢃⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿ ⣿⣿⣿⣿⠈⣿⣿⣿⢸⣟⣇⡌⣿⣌⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢃⣿⣿⣿⣿⣿⣿⢰⡟⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⣷⣿⣿⢸⡧⣿⣿⡙⣤⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣿⣿⣿⣿⣾⢃⣿⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⣿⣿⣿⢸⡅⣿⣿⣿⡘⣷⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠚⠃⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿ ⣿⣟⣿⣿⡀⣯⣿⣿⣿⡇⣿⣿⣿⣿⡈⣿⣯⣭⢟⢻⣹⣫⣭⡟⢿⣿⣾⢡⡿⣿⣿⣿⣿⣿⣿⢰⡟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡁⣿⣿⣿⣿⠀⣿⣿⣿⣿⢾⣇⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⢁⡿⣿⣿⣿⣿⣿⣿⣴⡏⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⣿⣿⣿⣿⡂⣿⣿⣿⣼⢋⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣴⠃⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡯⣿⣿⡕⣯⣿⣿⣿⡇⣿⣿⣴⠏⣿⣿⣿⣿⣿⣿⣾⠏⣿⣿⢸⡿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡁⣷⣿⣿⢸⡇⣾⣡⡟⣿⣿⣿⣿⣿⣿⣾⢃⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠆⡟⣿⣿⢿⣼⠃⡿⣿⣿⣿⣿⣿⣿⣼⢏⣿⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣿⣿⣿⡃⣿⣿⣿⣸⠋⣿⣿⣿⣿⣿⣿⣿⣱⠟⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⡃⣝⣬⣷⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⠕⣿⣾⣁⡟⣿⣿⣷⣿⣿⣿⣸⢃⣿⣿⣿⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣧⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡄⣬⢩⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠏⣿⣟⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⣮⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⡟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣯⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⣿⣿⣿⣿⣿⣿⣴⣋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣹⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠀⠀⠀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⣶⡞⢁⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢁⣠⠞⢻⡁⢻⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠤⢄⣘⣿⢬⣛⡷⢋⣈⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠙⠿⠀⢀⠿⠋⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡃⠀⢰⠀⠀⠀⡁⠀⡀⠀⠘⣆⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⣼⡦⠠⠤⣈⡆⢃⡤⠒⠙⡆⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⡇⢷⣄⣀⡠⠟⠛⠢⠤⠞⡟⠦⡀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⢀⠀⠀⠀⠳⡄⠀⠀⠠⡀⠀⠀⠘⠉⠙⠦⣀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠈⠓⢄⠀⠁⠀⠀⠀⠒⠂⠀⣾⠋⠉⠒⠢⢍⣙⡒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⡜⠀⠀⠀⠀⠀⠀⠱⡀⢀⡀⠁⠀⢀⡼⡇⠀⠀⠀⠀⠀⣏⠙⠯⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⢱⣀⣽⠶⠾⠛⠒⠛⠒⠒⠒⠤⠤⣸⡍⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⠢⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠥⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠤⠤⠤⠴⠒⠚⠉⠙⠢⣀⠀⠈⠑⠢⢄⡀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠚⠑⠢⢌⡓⠤⠤⠤⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠠⠤⣼⠇

●█▀█▄つε�🡈🝑🄤🡈🝑�⣿⣼⢃⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡘⣷⣿⣿⣿ ⣿⣿⢐⡾⣶⣤⣤⣴⢰⣵⣭⣭⣭⣭⣬⣶⣷⠂⣿⣿⣿ ⣿⣿⢣⡿⣿⣿⣾⢰⡀⣦⣷⣿⣿⣿⣿⣿⢿⠙⣄⣧⣿ ⣿⢶⡋⢟⠿⠾⠃⠟⠿⠿⠿⠿⡛⣟⣿⣿⣿⣿⠜⡠⣿ ⣼⡟⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡏⣿ ⠐⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠄⡏⣿ ⠝⡎⣿⣿⣿⢻⣆⣿⣿⣿⣿⣿⣿⣶⣤⣀⠄⠄⡟⣿⣿ ⣿⠻⡘⣤⣤⣤⢤⡄⣤⣤⣤⣠⠄⠄⠄⠄⠄⠃⣿⣿⣿ ⣿⣿⣿⣿⠻⠛⠐⠄⠄⠄⠄⠄⠄⠁⠉⠛⠹⡷⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⡸⣧⣿⡽⣿⣿⣿⣿⣿⣾⠅⣛⣽⣯ ⣿⣿⣿⣿⣿⣿⣿⠐⡤⣶⣤⣶⣶⣶⣶⣼⢏⣿⣿⣸⡞ ⣿⣿⣿⣿⣿⣾⣓⢇⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣧⡹ ⣿⣿⣿⣿⣿⢸⠼⠤⠤⠤⠦⠓⠄⣿⣿⣿⣿⣿⣳⣿⡿ ⣿⣿⣿⣿⣿⠸⢀⠄⠄⠄⠄⡄⠘⣽⣿⣿⣿⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⠈⠄⠄⠄⠄⠄⢸⣧⣿⣿⣿⣭⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⢹⠈⠄⠄⠄⢀⢄⡙⣭⣻⢸⣟⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣾⢀⠄⠧⠄⡇⣿⣻⠟⣻⢀⡇⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢈⠄⠃⢛⠄⡇⣾⣿⣕⣤⠰⠄⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⢀⠄⠄⣶⠠⡀⡐⠃⠠⡀⢀⠄⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⠠⠄⠄⠄⠄⠄⠄⠄⠐⠄⠄⠄⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠁⡟⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⠛⠉⠄⠄⠁⠄⠉⠛⠛⣿⣿⣿⣿

⠀⠠⠂⠄⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣹⢶⢊⠀ ⠀⠀⠀⠀⠈⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠞⠃⡿⣿⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⣝⠿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣚⢹⢂⠀ ⠀⠀⢀⠀⠀⠀⠄⠀⢀⠀⠂⢀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣞⣻⢬⡒⠄⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢋⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣷⣿⣷⣯⣷⣞⢫⣤⠒⣀⠐⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠈⠉⠛⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣆⡹⣔⠢⣁⠄⡁⠄⡀⠈⡀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣻⠙⠂⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠞⡠⢉⠈⠒⠉⣶⣴⢤⣤⣭⣾⣴⣤⣠⣀⣀⢀⠀⠀⠀⠀⡀⣀⣀⣄⣤⣤⣶⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠂⠀⠈⠂⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣻⠿⢛⠩⠙⠌⠋⠴⠤⣀⠀⠀⠀⠀⠀⠋⠶⡠⢀⠋⠔⡤⣀⢀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⣆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠐⢂⡁⠄⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠉⠉⠛⠛⠻⣾⢀⠇⠯⡰⢀⠀⠀⠀⠀⠀⢂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⣦⠿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢮⡙⠂⢈⠰⡍⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣀⣀⣤⠓⡈⣀⣀⣆⣧⣷⣿⢸⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠈⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠷⡙⠴⢊⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⣡⢢⠙⠈⠌⡀⣧⢹⡇⠿⢀⠀⠀⠈⠀⠀⠄⢀⠀⠀⢄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡒⢯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⡍⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢠⡄⡱⡀⡄⣿⠙⣽⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⡀⠰⠍⣿⣿⣟⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠲⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡆⣿⣰⣄⣿⣿⢻⡀⠢⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣆⣮⣿⠀⠀⣄⡙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿ ⠀⠀⠀⠀⠈⢀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣀⠘⠀⠀⢆⡿⠸⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢮ ⠀⠂⡀⠀⠈⡀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⣀⠀⠀⢸⠀⠀⢠⡆⢿⠀⠀⠀⡄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡳⠼⣟ ⠀⠐⠠⠄⠈⢂⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⢸⠀⠀⠀⠀⣠⢰⠀⠀⠀⠀⣀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠵⣞⢫⣵⡻ ⠀⠡⡀⠐⠌⢀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠋⠛⠚⠽⡷⣬⢞⣫⡵⢟⣣⡽ ⠀⠡⡈⠔⡈⠡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠚⠐⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠿⠯⡶⣟⣧⣹⣶⢛⣱⢺⡽⢞⣫⡵⣞⡯⢗⣫⡵⢻⣷ ⠄⠈⡑⠆⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣼⣻⣶⣛⢧⡸⣿⡓⣬⡟⢎⡽⢞⣫⡵⢞⣹⡾⣞⡳⣿ ⠡⢆⠁⢢⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣶⣷⣷⣼⣵⣰⣦⣀⣤⣤⣤⣶⣶⡿⣟⣫⣵⡺⢷⣎⠟⣣⣜⠷⣎⠷⣏⢲⣽⡼⢻⣷⣟⣿⣿ ⠄⡒⢉⡰⢏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣪⡱⢂⠷⡘⠣⡄⠃⢁⠦⠿⠿⠻⠿⡷⣜⢫⣱⡽⢫⢵⢫⢳⣬⢻⣭⢳⣹⣷⡟⣯⣟⣿⣿⣿⣿ ⡽⢟⡳⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡿⣾⢆⡉⠤⡎⢽⠢⡌⠑⠢⢁⠈⣀⣤⢶⣳⡿⣛⡽⠞⢫⡳⢭⡳⣜⠾⣝⡾⡽⣿⡿⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁⣿⣸⢆⠉⢠⠰⢻⢌⡙⠆⠬⡛⣈⢦⠳⠷⠿⠿⣿⣿⣟⢯⣳⣽⡾⣟⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⣿⡐⢢⠑⣈⠰⣿⣿⡿⢻⣟⠿⣛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡘⢌⠢⡌⠑⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢬⠒⢍⢂⠌⠣⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢳⣤⠴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡜⠈⣳⠌⡌⠇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⡐⢈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⢄⡑⠌⢃⡄⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡡⠄⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣶⣤⣤⣠⣀⢂⠒⢝⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡹⠱⡌⠓⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢂⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⣧⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣧⠾⠌⡑⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠱⢲⡍⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠟⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⠤⣿⢞⠣⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡸⢧⡘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣺⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢤⠞⣶⣤⣤⢦⠶⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠱⢾⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠼⠀⠀⠀⣼⠀⠋⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢶⣥⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⣳⡷⢯⡾⢳⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠔⠀⣀⣀⠀⠀⠀⠉⠋⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⡾⣡⠉⣉⢤⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠀⠀⠀⠀⠁⠉⠈⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣽⢿⣯⣞⠻⡈⣠⣀⣈⠄⠰⡉⣈⢀⠀⠉⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠇⡶⣤⣀⣀⣀⣀⣄⣤⢤⠒⠙⠀⠀⠀⠀⠀⠀⠀⠁⡔⢀⠀⠀⠀⠀⠀⠀⠜⣠⣤⣦⢳⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢾⣻⣽⣻⢷⣾⣟⡿⣳⣿⣷⣟⡾⣽⡿⢯⣳⢼⣻⡝⢻⣌⣷⡀⢹⣿⢨⠆⣿⢰⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⠒⠟⡿⣶⣤⢁⣼⠸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⢿⣯⢿⣾⣟⣽⣿⡷⣯⣷⣟⣷⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢯⣶⡽⣻⣽⢾⣻⣷⣻⣾⢿⣽⣻⢾⣻⣷⣟⣾⣿⢧⣙⡄⢱⡇⡌⢸⡇⣷⣾⡻⢿⠿⣿⣷⠽⠿⣾⣏⣘⠿⣧⠻⠁⠊⡞⣧⣧⢃⣥⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣽⡿⣷⢯⣽⣿⡿⣳⣿⣟⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣳⣯⣞⠷⣻⣷⣟⣯⡽⣿⢯⣽⢿⣯⣟⣯⡷⣞⢯⣽⡞⢻⡀⠰⠸⢠⠀⡇⢿⠙⠉⠉⠈⡏⡾⣿⢾⢠⡄⣿⠻⣾⢈⠇⢹⡇⡿⡛⣳⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⡿⣻⣿⣳⣿⣟⡾⣽⢿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣾⣽⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣛⢷⣭⣾⡟⣯⡷⣞⡽⢿⣯⡷⣞⣽⡾⣟⣳⣾⣟⡜⢿⡧⢾⠈⡆⠈⠀⡀⣿⣜⠳⠈⠀⣇⣿⣿⢲⠑⠞⣤⣿⠀⢱⣾⡘⡇⣿⡞⡿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣻⢿⣯⡿⣽⣻⢿⣷⣯⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣳⣿⣗⣯⣏⣽⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡳⢮⣝⡷⢏⣳⣯⣞⡿⣞⣻⣷⣟⣯⣟⣳⣽⢺⣷⣎⢻⣧⢿⠈⢆⠀⠀⢇⠄⡀⣦⠻⡛⢧⣧⠀⡃⣀⠣⣇⠈⣷⢡⢸⡟⣿⢎⡿⣿⣿⣿⣿⣿⣽⡿⣻⣿⢾⣿⣟⢿⣷⣯⡿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⡜⣻⢷⣯⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢮⣝⡹⢶⣛⣱⢾⣟⢯⣯⣟⣯⡷⢯⣳⣽⡿⣏⡳⣎⣝⠳⣧⢿⠘⢠⠀⠀⢣⠀⠀⡈⣷⡇⡆⠀⠀⠇⠀⢣⢸⡽⡞⢘⣿⣾⢏⣿⣿⣿⣿⣽⣻⣿⢯⣿⡷⣟⣾⣟⡾⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠲⣍⡖⢫⣵⡾⣛⣳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣥⡞⡝⣧⡝⣣⡼⢟⣫⢶⡿⣞⣻⣽⣾⡽⢿⣯⡽⣞⡛⣵⠺⣜⠳⠈⢂⠀⠀⢢⠀⡀⡀⠰⠠⢸⠀⡁⠋⡇⢼⣿⢆⡏⣾⢣⣟⣿⣿⣷⣞⡿⣳⢾⣿⣟⣾⣻⣿⣷⣟⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡁⠔⣊⠔⣫⡔⢻⣭⠷⣮⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⢮⡜⡝⢢⡼⣚⡷⢎⣳⣭⢷⣟⢯⣻⣷⣞⡿⣞⡿⣏⢳⣯⡝⢮⠱⣔⠳⠈⠀⠀⢆⠑⠀⠀⠃⠏⠟⡾⣷⡏⣷⢼⢫⣿⣸⢿⣿⣾⣻⣾⣟⣻⣷⣽⣾⡿⣟⣷⣟⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠂⢄⡈⠒⣁⠼⣏⡱⣿⢯⣾⣻⢿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⢆⣎⡙⢧⣎⡜⢻⣥⢻⣧⣝⡽⢯⡽⣻⣷⢟⣯⢶⣻⣯⠷⣛⢧⣹⡳⢌⣞⠧⠙⠈⡀⢦⠙⣊⣴⢺⢆⢃⣽⢯⡟⣭⢿⣯⣷⣟⣯⢷⣯⢿⣳⣾⣟⣽⣿⣟⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡌⠂⡑⠦⣩⡴⢻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢞⡌⠳⢦⣙⠶⣩⡼⢻⣧⡟⢧⣳⡽⣾⡟⣳⣽⢾⣻⣵⠾⣽⡞⢳⣯⡝⢳⡼⣟⣧⠾⡛⣝⣽⢯⣿⣷⣾⣿⢿⣷⢏⣻⣯⡷⣞⣻⢷⣻⣽⣿⣟⣯⡿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⡡⢆⡙⣧⡜⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡙⢬⡱⢮⡙⢦⣚⣜⡻⢧⣹⣷⢯⣳⣽⣻⣶⡿⣞⢯⣳⣽⡾⣟⣫⢶⡼⡿⣛⢷⣧⡟⣚⣽⡞⣹⣽⡺⢿⣏⠶⣻⢯⡷⣞⣻⣷⣞⣻⢿⣯⣟⡾⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡀⠀⢢⡔⡺⣝⣹⢿⣫⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⡑⢲⢎⡱⢮⢏⣩⢽⣯⡝⣻⢯⣽⡿⡟⣯⢻⣽⣻⣽⡿⣟⢯⣟⣯⣟⢯⡽⣻⣽⠿⣟⢯⣽⡿⡟⢯⢽⣻⣽⢿⣟⣻⣿⣟⣻⣿⣟⡿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠙⣿⣧⠀⣤⣶⣄⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣴⣮⡿⣿⡟⠛⠁⣙⠿⠿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⣿⣿⣿⣾⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⡇⢿⣿⡇⠈⠉⠻⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠧⠿⠿⠇⠀⠀⠀⠀⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⢿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⠟⠿⠻⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠉⠌⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⣿⣿⣿⠙⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡈⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣀⣦⣿⣿⣿⠹⣆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠻⣌⣷⣿⣿⢻⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⣿⣿⣿⣿⣴⢀⠀⠀⠀⠇⣿⣿⠙⣌⣤⣡⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡿⣿⣿⣿⢿⠻⠙⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣦⣿⣿⣿⣿⣿⠻⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣶⢠⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⣷⣿⣿⣿⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠁⡟⣿⣿⣿⣿⣿⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⠿⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣷⣿⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀

⠄⡇⣿⣿⣿⣿⣿⣿⠈⠄⣿⣿⣿⣿⣿⣿⠄ ⠄⠄⡇⣿⣿⣿⣿⣿⣿⢿⠄⣿⣿⣿⣿⣿⣿⠸ ⠄⠄⡇⣿⣿⣿⣿⣿⣿⣿⠄⣆⣿⣿⣿⣿⣿⢸ ⠄⠄⡆⣿⣿⣿⣿⣿⣿⢁⢸⢹⣇⣿⣿⣿⣿⢸ ⠄⠄⠄⣇⣿⣿⣿⣿⢰⡿⢻⣿⠹⣧⣿⣿⣿⠄ ⠄⠄⠄⠄⣷⣿⣿⣼⡏⣿⣿⣿⣿⠸⣿⣾⢂⠹ ⠄⠄⠄⠄⡀⣧⣾⠏⣿⣿⣿⣿⣿⢿⣀⠻⢧⣜ ⠄⠄⠄⠄⠄⠄⠟⣿⣿⣿⣿⣿⣿⢸⣧⡝⢤⠄ ⠄⠄⠄⠄⠄⠁⣿⣿⣿⣿⣿⣿⣿⢸⠿⠿⠘⠄ ⠄⠄⠄⠁⠞⣴⣩⣉⣬⣦⣷⣿⣿⢻⣧⣿⣴⠄ ⠄⠄⠃⡰⠟⣿⣾⣶⣷⢿⠘⢁⠟⠿⠻⣈⠄⠄ ⠈⠄⡼⡇⣿⣿⠄⠶⠁⣿⣼⡏⣿⣿⣠⣉⠄⠄ ⣿⠻⢋⡎⣿⣿⢿⠿⣾⣡⠟⣿⣿⣿⠺⣀⠄⠄ ⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣾⣩⣛⢘⠄⠄⠄⠄ ⣶⣴⣳⣛⣚⣎⢞⡋⡺⣷⣿⣾⣴⢀⠄⠄⠄⠄ ⠄⠄⠉⣍⢷⡔⢸⣵⠮⠾⠾⠙⠄⠄⠄⠄⠄⠄ ⠄⡟⣐⠤⠄⢓⡿⣹⢍⡙⡃⡆⠸⠄⠄⠄⠄⠄ ⠄⢸⠄⠁⡇⡄⣴⠠⣤⣉⡈⢸⢿⠄⠄⠄⠄⠄ ⠄⢸⢸⡷⡇⢹⡱⣢⠰⡙⠱⣿⣿⠄⠄⠄⠄⠄ ⠄⢳⣧⡎⡹⣷⡹⡸⠹⣿⡇⣿⣼⠄⠄⠄⠄⠄ ⠄⡀⢳⢌⣗⡿⣿⡿⣿⣿⣿⣴⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⡀⣄⣤⣤⣤⣠⣀⠄⠄⠄⠄⠄⠄⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈ ⠀⠉⠉⠉⠛⠟⠿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀ ⡀⣄⣦⣿⣿⣴⣤⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠛⠿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣼⠀⠀⠀⠀⣀⣦⣶⣷⣿⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠇⣿⠸⡦⣶⣶⣷⣿⠀⠀⠀⠀⡇⣿⣿⢷⣿⣿⣿⣿⣿⠺ ⠀⠀⠀⡇⣿⢿⠀⠀⠀⡏⣿⣿⢿⠉⠉⡇⣿⢿⡆⣿⣿⣈⣀⣀⢀ ⠀⠀⠀⡄⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠸⠋⠛⡛⣈⢁⠉⡍⣿⡻⣾⣴⢃⣿⣿⢿⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⢾⣿⣿⣿⣿⡆⣶⣴⣀⣧⢿⠘⡿⣿⣿⣼⠀⠀⠀ ⠀⠁⠟⣿⣿⣿⢸⣄⣤⣤⢠⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⢀⠀⠀⠀ ⠋⡿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⢸⠀⠀⠀⠀ ⣆⣿⡿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣍⣬⣠⠀⠀⠀⠀⠀ ⠀⣄⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⡉⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣶⣶⢀⠀⠀⠀⠀⠀ ⠀⡟⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣶⣶⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡀⣀⢤⠤⠦⠓⠚⠓⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠤⠤⡠⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⡀⣀⣀⣀⣀⣇⣀⣀⣄⢸⠀⠀⠀⠄⡸⣀⣒⣀⣀⣀⢀⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⢄⠑⠀⠀⠋⠖⠤⣀⣀⣀⢄⠢⠙⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⣀⢀⠀⡀⣀⠤⠒⠈⠀⠀⢅⡴⢀⠀⠀⠁⠊⠒⠀⠀⠒⣎⢿⠉⠟⡶⣤⠢⠟⠿⠛⠔⢀⠀⠀⠀⠀⠉⠂⠒⠒⠒⠓⠈⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢤⠢⡿⠀⠀⠁⠜⢀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠚⠠⣀⠀⠀⣀⠦⠈⠀⠁⠔⣀⠀⠀⠃⡴⠀⠀⣄⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣧⢤⠒⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠛⣰⠀⠀⠀⠎⢠⠀⠀⠀⠀⢇ ⠀⠆⠈⠀⠀⠀⠀⠟⣶⣸⠀⢄⠳⡏⠘⠀⠀⡀⣀⢤⠦⠒⠒⠙⠉⡏⢸⡀⠣⠙⠀⠀⠀⠀⠀⡟⣿⢴⠳⠀⡇⢀⠀⠀⠀⠀⠁⣸ ⠀⠀⡀⠦⠙⠉⡉⣸⠀⢆⠉⠉⠉⣖⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⣄⣤⠤⠤⠤⠤⣿⢀⠀⡏⠁⡟⠀⠀⠀⠀⠁⡴⠀ ⠀⠀⠀⠀⣄⢹⡀⣆⠙⠀⡇⢰⠁⠞⣠⠀⠀⠀⠁⠾⠴⣠⣀⡀⢀⣼⣀⠦⠓⠈⠀⠀⠀⠀⠀⣿⠉⡔⢀⡀⣿⢶⠙⠉⠜⣀⠀⠀ ⠀⠀⠀⠀⠀⡀⠳⠀⣇⢾⡠⠃⣠⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠏⢀⠀⠞⡠⡀⢄⠢⠈⠀⠀⣦⢹⠈⠁⠋⣾⠀⣏⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢣⡈⢹⠀⢰⠀⠀⠋⠔⣀⠀⠀⠀⠀⠀⠃⡼⣿⠀⡇⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⡀⣄⣽⠀⠏⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⠻⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠟⣾⢀⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⡄⣿⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣘⢢⠙⠀⠀⠀⠀⠀⠀⠁⡟⣿⢸⠀⡄⢳⢹⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠙⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⣀⢄⠦⠽⠤⠠⡂⣿⣧⠸⠀⠀⡀⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢏⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠑⠉⠛⡖⠤⠤⠤⣿⠻⠘⣀⢀⠤⡧⣿⢾⠓⠉⠈⠀⠀⠁⠉⠚⡯⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣨⣀⣄⠹⠊⠔⡦⣿⢶⠶⠶⠷⣿⣴⢀⡀⡀⣦⣽⣀⣷⣿⣈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣠⣆⢻⠈⠀⡞⠀⠀⠀⠀⣀⣞⣤⣯⣠⠀⠁⠚⠐⠀⡀⢧⡟⡾⣶⣤⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠚⠒⠒⡖⠻⠈⠀⡄⢿⡿⢲⠛⠓⠑⠈⡴⠃⡴⢁⠊⡴⢀⠀⠀⠀⠀⠀⣄⢿⠉⠟⢻⠒⠙⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡿⣾⢤⣠⣀⢀⢀⡀⢯⣾⣠⣿⣿⣿⣝⠻⣅⠾⣡⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⠈⠀⠤⠤⣤⢷⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣦⠘⠀⠀⠁⠉⠿⠿⣿⢹⡍⣿⣿⣿⢿⡟⣴⠎⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⡏⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢄⠯⣶⣲⣷⣾⣶⣶⣶⣶⣶⣿⣴⢁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠓⠛⠖⡤⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠞⣠⢁⠊⡴⣀⠀⠀⠀⠀⠁⡞⢠⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⠀⡓⢿⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡼⠁⠞⣠⠀⠀⠀⠀⠀⠀⠏⣠⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡀⣄⢿⠘⠀⠀⠀⠀ ⠀⠀⠀⠁⣿⠛⡰⠀⠀⠀⠀⠀⠀⠁⡜⢀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀ ⠀⠀⠀⡇⣾⢠⠂⠴⢀⠀⠀⠁⠊⡦⢙⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⢸⠀⠀⠀⡀⠢⠈⡆⢸⠀⠀⠀ ⠀⠀⠀⡆⢲⠓⠉⠊⠒⠔⡤⣀⠀⠀⡀⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡴⢀⠀⣀⠤⠲⠛⠉⠉⡉⠋⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠉⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠚⠒⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠽⠤⠤⠤⠶⠒⠛⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⠟⠶⠴⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⢄⠤⠤⠦⠶⠒⠒⠓⠉⠉⠉⠉⠈⠉⠛⠿⠿⠭⠦⠶⠻⡈⣻⠈⠀ ⠀⠋⠟⠿⣷⣞⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠖⣤⣷⣏⣿⣥⣀⣷⣿⢿⣿⣿⣄⢻⠀ ⠏⢲⠑⣋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠽⣿⣠⠀⠀⠀⠂⣍⣷⠈⠀⣇⣯⣿⣾⢀⠀⡇⠘ ⣦⣿⠽⠙⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡤⣠⣀⣀⠁⠚⡴⣤⣷⠀⠀⠁⡒⣖⡶⢶⢯⠀⠀⣄⣶⢀⠀⠀⡏⣾ ⠀⣄⣦⡿⣛⢮⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⡿⣉⠈⠀⠀⡇⠀⠃⣰⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠂⣾⣤⣀ ⠀⠀⠀⠀⣀⢤⡤⣦⠶⠷⠓⠛⠛⠛⠒⠗⠼⡤⣀⠀⠀⠀⠀⡀⣄⢷⠿⡬⠻⡟⠈⠀⠀⠀⠀⠀⠁⣟⢹⠀⠀⠀⣝⠹⠀ ⣀⣀⢤⠦⠲⠛⠛⠖⠴⡠⣀⣉⠚⠐⠁⡰⠀⠀⠀⠄⠤⠘⠀⠀⠀⠀⣧⡼⣀⢀⣦⠘⠀⠀⠀⠎⣿⣿⣿⠿⠙⠀⡄⣿⠀ ⠀⠀⠁⠚⡴⣀⠀⠀⠊⡠⣀⠀⠀⠀⡁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇⢰⠚⠷⠭⣎⢳⠈⡜⠀⡄⣿⣿⣶⡽⢾⡴⢀⠀ ⠞⡭⢀⠀⠀⠀⠀⠇⢀⠀⠀⠁⠊⡴⢀⠀⠀⠀⠀⢻⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⣄⠳⠈⣆⢸⠉⠋⣴⡤⣀⠀⠀⠀⠀⠀ ⠈⠒⣔⠲⠉⠀⠀⡀⠁⠊⠔⣠⠀⠀⠀⠀⠀⠀⠃⣾⢠⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⡇⢸⠀⣄⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢄⠑⡬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠃⣰⠀⠉⠉⠀⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⢄⠱⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⡽⠋⠴⣀⢀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠱⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⠀⡞⣠⢀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⣄⢷⠿⠺⠶⡟⢰⠀⠀⠀⠀⠏⢠⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠙⠉⠀⠀⠀⠀⠀⣄⠳⠏⢰⠀⠀⠀⠀⠇⣰⠁⠉⠉⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⡷⠸⠀⠀⠀⠀⠀⡀⣦⠸⠀⠀⠀⢿⣰⠀⣸⠀⡝⢹⠉⠒⣴⣧⢽⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢰⠀⠀⠀⠀⠓⠈⠀⡇⠘⠀⠀⣼⠀⠏⢹⠉⡿⣴⠀⠀⠁⣾⣥⣊⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⡄⢸⠀⡇⢰⠀⡇⢘⠎⢀⡟⣿⣠⠀⠀⠀⡀⣋⣻⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠃⣲⣾⢀⠀⣿⣰⠀⠀⠀⠀⠓⣿⣟⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠃⣠⡞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣄⣷⣹⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠏⣨⡞⢀⠀⠀⠀⡇⠐⠋⠙⠈⠀⠁⢀⠀⣄⣦⢳⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠁⣹⡴⢀⢆⢳⠀⠗⠺⠀⠀⡃⣭⣷⣿⢿⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿⣰⠀⠀⠀⡀⢦⠉⠊⠠⠰⡟⡀⣮⣿⣿⢠⠀⠀⠀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⢠⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⣿⡞⣶⣧⢰⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⢶⡷⢻⣾⢸⠀⠀⠀⠀⠀⠀⡀⢳⠏⠖⣠⠀⠀⠀⠀⠀⠀⡏⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⣰⣀⠀⡀⢿⢻⠛⠤⠤⠛⠉⠉⠉⠀⠁⠉⠈⠀⠀⠀⠀⠀⠞⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠇⣴⠸⠀⠀⠃⣰⡀⣇⣵⣠⠁⠞⣀⠀⡃⣻⢔⠠⠀⠀⠈⠋⡰⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⡾⢠⠀⠀⠃⢰⠇⢀⠀⠀⡼⠀⠀⡟⢠⠇⣴⠀⠀⠗⣸⠀⠀⠀⠀⠁⣾⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⣀⠀⠀⠀⠁⡹⡼⢀⠀⠀⠏⢀⠀⠇⢸⠀⡘⠀⠀⠀⡼⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⡾⣧⢀⠀⠀⠀⣾⠀⠀⡇⢀⠀⢸⠀⠀⠁⢸⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠃⢰⡇⠀⠀⠀⡇⢀⠀⠀⡇⢸⠀⢇⠀⠀⡄⢸⠀⠀⠀⠏⣰⠤⠑⠉⠀⠀⠁⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⡗⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⣧⠈⡀⢲⠀⠀⢸⠀⠁⡞⢀⠀⠀⠀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⣧⠃⢰⠀⠀⠀⢸⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⢸⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⡇⡸⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⢄⠙⠀⠁⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⡇⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠉⠘⠁⡏⢀⠁⠰⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣵⠁⡹⣰⢿⡨⠏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⢀⠀⠀⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠏⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡼⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠸⠀⠀⠃⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡆⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⡜⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠁⢰⠀⠀⠀⣄⠙⠀⠀⠀⠀⡀⢠⠀⠀⡄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⠀⡇⠀⠀⠀⠀⠀⡀⢤⠑⠀⠀⠀⠀⠀⠐⠀⣾⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠀⡽⠉⠒⠒⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢠⠀⠁⡴⣀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠋⠴⣠⢀⠀⠀⣀⢤⠑⠀⠀ ⠀⠀⠀⠀⣾⠀⠁⣰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢷⠀ ⠀⠀⠀⠇⢀⠀⡇⠀⠀⠵⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠛⡀⢸ ⠀⠀⠀⡸⠀⠀⡄⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡂⣠⠇⢠ ⠀⠀⡎⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀ ⠀⠇⢠⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠘⠀⠀ ⠃⡼⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⢸⠀⠀ ⡆⢹⠀⠀⠀⠀⠀⠀⠀⠧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⠀⠀ ⠀⡄⠑⠀⠀⠀⠀⠀⠀⡀⣧⠉⠉⠉⠉⠉⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠀⠀ ⠀⠀⠀⣀⠯⠿⠛⡈⣀⣀⣀⢻⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⢞⠓⠔⠾⡠⢀⠀⠀⠀ ⠀⠀⠀⡞⢏⣎⣇⣀⢯⠑⠀⣿⠀⠀⠀⠀⠀⠟⠊⠟⡼⢀⠋⣠⠎⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣼⢰⡇⠀⢸⡞⢣⣼⠀⠀⠀⠀⡇⣹⠈⠷⢀⠟⢳⠏⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⣿⠀⡀⠸⢻⢸⡇⢀⠀⠁⠖⡠⢀⠀⡀⢄⡶⣟⡀⡼⠳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠸⠀⢇⡆⢘⡇⠀⡤⢀⠀⠀⠂⠒⠶⠰⠈⡀⢦⢻⠀⢦⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠈⡀⢹⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠀⠀⡄⠘⠀⢇⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢸⠀⣇⡽⣴⠘⠀⠐⠛⠛⠐⠀⠀⠀⣀⣻⢟⠉⣏⠹⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⣹⡇⠀⢣⠋⠸⣷⢼⢱⠛⠀⠀⠀⡦⣶⡛⣾⡇⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⠈⣿⠀⡅⣹⣤⢿⣶⣤⢀⠙⠘⠀⠆⠓⡟⣾⣠⢳⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⣄⣧⠈⠀⣆⣸⡿⠢⠶⣤⣠⠀⠀⠋⡳⣰⠀⠀⡎⠇⢾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⡄⣗⠘⠀⠀⠉⠚⡥⢚⣠⠀⠀⠁⢸⡞⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⡀⢦⠤⣠⢀⠴⣠⠀⠀⠀⠀⡥⡞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠁⠉⠚⠴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣇⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⡀⣏⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⣤⣶⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⡿⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣤⣊⣗⡿⣶⣠⢀⠀⣄⠶⠙⣌⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠗⠿⣴⢀⠠⠀⠀⠀⠀⠀⠀⣄⠦⣟⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠆⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⢿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⢿⡘⣀⢤⠢⠒⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⣿⣿⣿⣿⠻⠈⠀⠀⠀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠶⠤⠤⡀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣠⣀⣷⣿⠿⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⢹⠆⡿⣿⣾⣿⣿⣿⠿⠭⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⢠⡷⣅⣮⣷⣿⣿⠿⠻⠒⠛⠛⠙⠉⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⣿⣿⢿⣒⣽⣮⣶⢶⠷⠛⠐⣤⣀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣠⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⠸⠀⣀⢤⠤⠲⣒⢒⠐⠋⠛⠒⠒⠴⠤⣀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠻⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠋⡶⠿⣿⣿⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⣀⣤⣦⣴⠷⣜⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣠⢄⠦⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣰⠀⠀⠀⠀⡀⣄⠦⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀

⢠⡔⠊⢄⡉⡐⢦⣿⡟⣧⢿⡹⣶⡼⡝⢲⡹⣵⣾⣿⣿⣿⣿⣿⣟⢿⡻⣟⢏⣩⢶⣭⡲⣝⣲⡼⢟⣡⠷⣎⡝⢧⠮⣙⢮⢳⢧⣊⠷⣏ ⣂⠄⠌⢂⠑⡠⠄⡈⣶⢿⣮⡿⢎⣜⡹⡼⡜⡳⡖⢎⡱⣖⣬⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⡻⢿⣟⡛⣹⢳⣭⡞⢫⢵⢮⣝⡻⢿⣯⣿⣿ ⠡⣂⠁⢂⠠⡐⢂⠄⠂⡀⣧⣞⢿⣎⠳⣎⡕⢪⡵⢚⣡⠶⣌⡙⡣⣤⣼⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⢭⡾⢏⣱⡼⣛⡷⣟⢯⣿⣧⣚ ⡈⠐⡈⠐⢂⡀⠐⢈⠠⠐⢈⠂⣄⢿⢮⡕⢪⣜⠳⡌⣃⠴⢎⡑⠣⢆⡄⠘⢣⠁⣩⣍⣭⣶⣻⣶⡿⣽⢿⢯⣜⡻⣞⠷⣯⡵⢎⡱⢪⡐ ⢿⠉⠀⡐⠄⡈⠂⠁⢀⠠⠌⠀⠐⡀⣷⠹⢳⣌⠳⣉⢰⡹⢄⡩⠟⡶⣴⣤⣤⣤⣤⣤⣦⢶⡷⢿⡙⣺⣄⣷⣶⣿⣿⡟⢐⣡⡔⠂⢀⠀ ⡙⣄⢷⠙⠠⠀⢀⠈⠡⠀⠐⠠⠂⠄⡀⣧⡹⡖⢊⡰⡞⠃⣾⣢⢀⠀⠀⠀⠈⠐⠀⠁⠂⠀⠈⡀⣀⣦⠻⠀⠂⣤⣲⢀⡈⠀⠡⠄⠡⠀ ⡖⢎⠓⡟⢶⡙⠀⠀⠈⠂⠄⠀⢁⠀⠠⠈⣆⢿⣎⡌⠗⣿⢡⠂⠄⡀⠁⠄⠀⠈⡐⠁⠄⠂⠁⢂⠀⠐⠈⢀⠐⠂⠀⠂⠄⡀⠐⡈⠒⠀ ⣊⡅⢛⡿⣿⣿⢿⠙⠀⠀⢂⠁⠠⠀⢀⠈⠐⡄⢿⣍⡡⣷⠸⠁⡀⠐⠠⠐⠌⠂⡀⠐⡘⠄⠈⠰⢂⠐⠁⠠⠌⠀⠐⠀⢂⡁⠄⡐⠒⢀ ⡽⣿⣾⢿⣿⣿⣿⣟⢷⠙⠀⠀⠐⠠⢀⠂⠄⠀⡄⣻⡽⡎⣷⠈⠄⠃⢀⠠⠐⢁⡌⠂⠐⢣⡄⠘⢣⡀⠑⠠⠐⠌⡀⢰⢂⠁⠤⡈⠰⢈ ⣿⣻⣿⣿⣟⣿⣿⣿⣻⣞⢻⡀⠀⢂⠄⠀⠠⡐⠄⡀⣀⣤⣷⢿⡙⠀⡐⠌⡁⠠⠌⠣⣀⠱⢂⡌⠐⡨⠒⡈⠄⠈⠀⠡⢀⠡⠄⢈⠤⠈ ⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⡽⢿⠙⠀⠠⢈⠂⡀⠐⠂⢀⠈⠀⣄⣿⢿⠙⠄⠁⡄⠊⢁⡠⠘⢢⠑⠆⢁⠠⠐⢈⠐⢁⠀⡐⠁⠠⠐⢂⠀ ⢣⣶⡝⣯⡟⣿⣫⣽⣳⣿⣿⡽⣿⠘⠀⠐⠠⠀⠠⠄⠀⠌⠁⠀⡀⣷⣿⣮⠻⠘⠄⠀⢠⠒⢄⡉⠂⢀⡐⠌⠁⠠⠀⠈⠀⠀⠈⡐⠀⠒ ⣳⡽⠧⣿⣿⣿⢻⣳⣿⡽⣿⣿⣾⣿⠘⠀⠡⢀⠌⡀⠀⠁⠉⠈⠀⡀⣷⣯⠻⣭⣶⠿⡉⠀⢄⠀⠡⢀⠠⠀⠈⠀⠆⠀⡀⠀⠀⠀⡉⠴ ⣿⣹⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⢸⣷⢿⠈⠁⠈⠀⠉⡟⣿⣻⣟⣿⢽⡿⣩⠶⣎⣿⠿⣿⢺⠀⡀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡀⣷⢸⡄⢻⠉⣀⠇⣿⣿⢾⣂⣠⣄⣤⣦⢶⣶⡶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⡧⣙⣿⢸⠐⡄⢿⡈⣿⣇⠹⡆⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣧⣾⢆⣆⣤⣴⣦⠀⡆⣿⣿⠀⠂⠀⡀⣄⣶⣻⢻⠉⣆⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠼⠟⠘⢀⠂⢀⠌⠂⠌⠀⣇⣺⠀⠁⠀⢈⠀⠀⡟⣼⣿⢿⡛⣮⠻⠉⠈⠀⠀⠀⠀⠁⠉⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠶⠜⠰ ⣿⡈⣿⠁⠿⠻⠚⢩⢑⠠⡏⢸⠀⠀⠐⠈⢀⠀⣿⣿⣿⣿⣶⣷⣨⣀⣄⣤⣤⡴⣤⣠⣀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠟⡽⣮⢃⠤⡘⢌ ⣿⣹⡟⢣⣧⣿⢿⢋⡱⡏⣿⢸⠀⡐⠂⠌⠁⠀⣿⣷⣿⠀⠀⠀⢀⠀⠀⠂⠀⠀⠈⡀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠁⡾⣬⠓⠤⢋⡤⠚⢌ ⣿⢿⣿⠸⠁⣽⢴⢋⡿⣿⣿⢘⢈⡐⠄⠌⠈⠃⣽⣿⣾⠀⠁⢂⡀⠈⢀⠌⠀⢁⠀⠈⢀⠀⠂⣰⠀⠀⠀⠁⠟⣼⠖⣉⠲⣍⠒⣩⠖⢊ ⣿⣿⣿⢻⡿⢻⡿⣿⣿⣿⣿⠼⠆⡁⢊⠔⠈⡇⣿⣽⢠⠐⠈⠂⠁⠄⠀⠀⠄⠀⠈⠀⠀⠐⢀⠀⠀⠁⠛⣼⢲⢎⣌⡙⠶⢋⢦⡙⠧⢎ ⣽⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣻⢄⠡⢌⠣⠀⣯⣰⠐⡡⠄⠂⢁⠠⠀⡨⢆⠈⠄⠀⠀⡀⠀⠁⠉⠟⣼⢳⣌⠶⢎⣙⠳⢬⢓⡬⠓⢣⡕ ⣻⢷⠎⠁⣎⣀⣯⣿⣿⣶⢭⣿⣿⠹⠤⢊⠡⢐⠡⡔⠈⡠⠌⠐⠡⢂⠄⠀⠉⠛⠻⠟⠷⣽⣶⣍⠳⣌⠳⣌⡽⢎⡱⠶⣍⠳⣌⠳⣢⡞ ⣿⣿⢿⢿⠿⣿⣿⣼⣿⣿⣿⣿⣿⣿⢿⠻⢛⡉⡐⠆⡀⠔⢂⡁⠉⠛⠟⣯⣜⠻⢧⣙⢮⡝⡳⢎⡹⣜⡻⣍⠳⣎⣙⢳⢭⡳⣍⡹⢯⣏

⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠋⡿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣷⣎⣿⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣐⠋⡾⣫⡾⣤⢀⠁⠉⠛⠛⠶⠶⠹⠀⠀⣂⣤⣿⣾⣴⢀⡼⠀⣆⣿⣿⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣸⠟⣫⡾⣠⠋⠟⡶⣤⣀⢁⠛⠖⠤⠀⠉⠛⠶⣤⣀⠀⠉⠟⢸⠀⠀⡀⣤⣷⣿⠿⠛⠛⠛⠛⠛⠛⠟⠿⣿⣿⣴⣤⣤⣤⠳⠈⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡞⢟⣿⠾⣴⣀⠀⠉⠉⠉⠉⠛⠽⡯⣹⢉⠛⠛⠟⠿⣿⣾⣠⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣶⣶⣴⣤⣠⢋⡿⢘⠀⠀⠀⠀⡀⢠⠀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣠⣀⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡴⢀⡈⢿⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⠖⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣾⣠⣄⣀⣷⣽⣉⢋⣛⣛⣛⣛⣿⣾⣴⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⠠⠀⠄⣷⣾⣶⣶⣷⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠻⠛⠙⠉⠉⠀⠀⠀⣀⣿⠿⠌⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠉⠀⠀⠀⠁⠉⠛⠖⡤⣠⢀⠀⠀⣆⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡆⣿⣿⣾⡇⣿⢿⠻⠛⠟⣾⣧⣿⣿⠀⠀⠀⠀⠀⠄⠲⠀⠀⠀⠏⣾⠶⣻⠛⠙⠗⡿⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⠻⠉⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣆⣿⣿⡟⣴⠈⠏⣿⣴⠋⣿⣿⣿⢿⠻⠛⠁⠉⠉⠉⠉⠋⡴⣠⠀⠀⠀⠀⣀⣧⢸⠀⠀⠀⠀⠁⠛⠿⡶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣄⣿⣸⠀⠟⣼⢋⡟⣿⣴⣀⠀⡀⣄⣦⠻⡛⠙⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠟⣾⣠⠉⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⠈⠀⡀⣤⠷⣽⠏⣿⣿⢴⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⢿⠻⠙⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⡟⣼⣿⢾⣙⣄⠲⠛⠒⠑⠞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣿⠙⠀⠀⠘⣇⣭⣶⣳⠉⠀⠀⠀⠀⠀⠀⠀⠉⣯⣼⣿⣿⣿⣤⠿⠬⡿⣴⢀⠀⠀⠀⢩⣿⠀⠢⣆⡻⣍⢦⠰⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣦⣯⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⠻⠈⣄⣿⣮⡟⢸⡟⣿⣿⢥⠀⠇⠿⣿⣟⣿⣿⣾⣠⡏⠿⣸⢀⠀⠀⠀⠀⠁⠉⡟⣿⡿⢿⠿⠻⠛⠛⠾⠶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢹⣧⣿⠿⡿⢿⡙⣮⣿⣿⣿⣿⠉⡿⣼⣿⣿⣿⣴⢁⡟⣿⣏⠸⠀⠀⠀⠀⠀⡀⠋⠻⣿⠘⠀⡄⣿⢸⡀⣄⢦⡛⡋⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠻⣀⢦⣙⣤⣶⠿⡛⣏⣼⣷⣿⣿⣷⣿⣾⢁⠞⣡⢟⣿⣿⢻⠈⡀⠈⠀⠀⡇⣼⣤⣷⢹⠀⠁⣿⢠⠀⠀⠀⡀⣅⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠻⠙⢉⠈⠀⣀⣄⣶⣿⡛⣯⠹⣇⠿⣵⢞⣾⣷⣿⣿⣿⣽⠀⠀⠀⠀⡀⢳⠈⡀⣧⠸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠐⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣙⣀⣄⢤⠿⠶⠛⣙⣿⣿⣻⡍⣿⣾⠶⠀⡀⣦⣷⣟⣿⠲⠒⠙⠉⠀⣄⢦⠓⢈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡎⠘⣛⣛⣛⣿⣿⡿⣾⢷⠈⠀⠀⠀⡀⣶⢠⠀⠀⠀⡀⣀⣤⠦⠒⣗⣯⣿⠈⡀⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⣿⣿⣿⣿⣿⣾⢀⠀⣇⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠲⠛⠙⠉⠈⠀⠀⠀⠀⠀⡇⣿⡇⣿⢸⡅⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣸⣽⣀⣴⣿⣤⣶⣵⣤⣠⣀⣀⣦⣶⣦⣿⣴⠖⠠⠋⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢦⠶⠿⠛⡛⣿⠉⣿⢨⡀⡰⣷⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣖⡤⣀⣏⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠒⠒⠐⠀⠀⠀⠀⠀⠀ ⠄⣠⣀⣿⣿⢿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠁⠋⠖⣠⠂⠿⠤⠤⡤⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣿⣿⣧⣿⣿⢿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠁⠚⠶⣻⢉⠈⠀⠁⠉⠉⠋⠛⠒⠒⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣱⣿⣄⠳⠈⠀⠀⠀⠀⠀ ⠀⠃⣿⣾⣶⣠⣀⠀⠀⡁⣍⣯⠻⠙⠀⠐⠀⡄⣠⠀⠀⠀⠁⡋⣴⣀⢿⠻⠉⡀⣀⣄⠦⠒⡀⣄⢷⠿⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣥⣴⠃⠿⢸⠀⠀⠀⠀⠀ ⠞⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⣿⠿⠻⠟⠤⡤⣤⣀⣀⠀⠀⠀⡀⣀⣠⣤⠦⠙⠈⠀⠀⠀⠀⣯⠀⠀⣄⣷⢬⠦⠓⠛⠉⠉⠉⠈⠀⠀⡄⠹⡆⠸⡏⣠⢸⠀⠀⠀⠀⠀ ⢸⡀⢸⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⡿⣷⣿⣜⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠶⠶⣿⢿⠻⠙⠋⣾⠻⠈⠀⡀⣦⠙⠀⣄⣿⣿⣙⣀⣀⣀⢀⣦⠙⣦⢻⡜⢀⠀⠀⠀⠀⠀ ⢰⠀⢧⠀⠀⡆⠸⠀⠀⠀⠀⠀⠏⣾⣫⣴⢁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣇⣿⣽⣟⠀⡀⣦⠹⠀⠀⡀⢳⠀⡄⢹⣿⣿⢿⠟⠭⠾⡒⣖⣽⠈⠀⠀⠀⠀⠀⠀ ⠘⠀⡄⢸⠀⠀⢸⠀⠀⠀⠀⠤⣷⢾⣡⠞⣠⠀⠀⠀⠤⠳⠛⠀⠀⠁⡾⠦⠓⠉⠀⠀⠁⡟⣼⡟⢸⠀⠀⠀⡀⢧⠈⠀⡀⢧⠈⡇⣧⣿⣼⣦⣴⣤⢷⠳⠙⠈⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⢿⠀⠀⣦⠘⠀⠋⢿⡿⣱⠞⣠⢀⠀⠀⠀⠀⠀⠀⣄⢰⠀⡄⢳⣯⠉⣿⢹⡻⣿⣶⢁⡿⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⢧⠈⠀⢳⠀⠀⠀⠀⠀⠀⣄⣴⠶⠙⠀⠀⠀⠀ ⠀⠀⠀⣄⠱⠀⠀⣄⠳⡾⣥⢞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣿⣽⢋⠗⣾⣦⢷⠻⠀⠀⠀⠀⠀⡄⠹⠀⠀⢧⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⡄⢧⠙⠀⠀ ⠀⠀⠀⠀⡀⢧⠈⠇⡈⢶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢉⡾⢤⡤⣋⣴⢷⠙⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣞⢷⠙⠇⢠⠀⠀⡀⢦⠙⠀⠀⠀⡀⠱⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠹⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⣄⣤⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⡄⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⡷⠀⠁⠿⡿⢽⢀⠀⠁⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢣⡌⢹⠀⢻⡟⣿⣿⢸⠁⠟⣼⠃⡒⣗⠻⡗⢿⠃⠘⠀⠛⡿⣶⣒⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⡇⣧⣛⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠏⢀⡀⢧⣿⠹⣆⣸⠀⡏⢾⡤⢀⣄⠳⢻⣿⣿⡿⣼⠇⢰⠇⣼⣄⢿⡽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡾⡿⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠁⡞⢀⠀⠀⠀⣦⣽⠳⢳⠀⡀⠸⠀⠀⠀⠀⠀⠉⡟⣾⠀⣰⠎⣤⢻⡼⢀⡀⣄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣹⠉⠉⠉⠉⠋⠒⠒⠄⠀⠀⠀⠀ ⠀⠀⠟⣿⢮⠈⠀⠀⠀⠀⣆⡙⣧⢻⠀⢻⠀⠀⠀⠃⡓⣿⣼⢀⠋⡴⢀⡤⣠⠀⠀⠀⠀⠀⡀⢤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⣿⣿⢸⢇⣞⠙⠀⠀⠀⠀⣄⠘⣆⠹⣶⢿⠹⠏⡿⣾⣠⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠲⠉⠀⠀⠀⠀⠀⠀⠀⡀⠁⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀ ⣿⣿⣿⣿⡀⣞⡛⠳⠈⠀⠀⠀⡄⠳⡀⢦⣝⣿⣿⣥⠞⠫⡴⣄⣤⠲⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠏⠈⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⣶⣶⣷⢻⡌⡳⢻⢈⠀⠀⠀⠀⡀⢦⠈⡀⣷⢙⣋⡽⢀⠀⠀⠀⠀⠀⣀⣄⠦⠲⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⣾⢁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⠀⠀⣀⣄⠳⣉⣤⠳⠈⠀⠀⠀⠀⣄⠀⠀⣄⢲⣝⢤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠒⠐⠀⠀⠀⠀⠀⠀⠋⣰⠀⢋⡴⠀⠀⠁⠀⠭⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣀⣄⠤⠤⠲⠓⣙⢌⡤⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠓⡈⣄⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡴⢀⠀⠏⣠⠀⠀⠀⡀⡿⣿⣿⣾⢐⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠲⠉⠀⣀⢤⠀⠀⠀⠀⠀⠁⠉⠉⠉⠞⡤⢀⠀⠀⠏⢠⠀⠀⠀⠀⡀⣲⣒⣄⣀⠀⠀⠁⠈⠀⠀⠀⠀⠀ ⣤⣳⢽⠬⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠉⠛⠒⠤⡤⣤⣠⣀⣄⠦⠙⠀⠁⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⠝⠰⠀⠀⠀ ⠀⠀⡀⣄⢦⠓⠉⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠑⠈⠀⠀⠀⠀⠀⠀⠉⠖⡴⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⠢⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⠈⠀⠀⠇⣼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣲⠀⣤⣠⠀⠀⠀⠀ ⠚⡴⢸⠀⠀⠁⠋⠖⠴⠤⣤⣤⠦⠲⠛⠉⠀⠀⠀⠀⡇⣸⠀⠀⠀⣣⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⣇⠀⠀⣠⣀⣀⣀⣀⣀⣤⣤⠤⠲⠒⣒⢉⠉⠈⡀⢸⠀⠀⠀⠀⣄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠒⡭⣠⣀⣄⢦⠙⠀⠀⠀⠀⠀⣀⢤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⢧⠈⠀⠀⡀⢦⠙⠈⠀⠀⠀⠀⠀⠀⣀⣄⠦⠶⠲⠛⠉⠉⠉⠉⠋⡼⢀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢢⡿⢸⠀⣯⠈⠀⠀⠀⠀⣄⢤⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⣸⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣷⠇⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢳⠀⠀⡀⣆⣠⠀⠀⡏⢀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠏⡿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣜⣷⣿⣦⣷⡿⣿⣾⣿⣿⡿⣿⣿⠚⣿⣸⠀⠀⡆⢸⢻⠀⠀⠃⡿⣻⣿⣰⢁⠋⠟ ⡀⠳⠀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀⠁⠚⡴⣠⣀⣀⣀⣤⣤⣦⣾⣿⣿⣿⣿⣴⣤⣦⡿⣿⢿⡘⣷⢻⠈⠀⣀⣤⣷⣿⣿⣿⣿⠈⣿⣿⠀⠀⠀⢸⡇⠀⡟⣯⣷⣾⣡⡾⣠⠀⠉ ⠀⠀⢣⠈⠀⠁⠏⣠⠀⠀⠀⠀⠁⠟⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⣀⣤⢤⠲⡓⣯⣿⣿⠘⢀⢦⠙⠀⠀⠀⣄⣿⣮⣿⢀⣿⣿⢿⠿⢸⣿⡇⡿⣿⣠⡿⢳⡿⢁⠟⣿⣾ ⠀⠀⠀⣄⢦⣠⢀⠀⠀⠀⠁⠞⣠⣄⠀⠀⠀⠀⠁⠉⠉⠉⠉⠋⡰⣀⣀⠦⠙⠀⠀⠀⠀⠀⣄⣦⣿⠙⠎⣟⢿⠙⠀⠀⡆⣿⣿⠘⣿⣿⣿⣿⣿⣧⡇⣿⣰⠏⢰⡏⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢠⠀⠀⠀⠀⠀⠋⡴⣀⠉⠉⠋⣴⢀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⠀⠀⡀⣶⢻⡈⣯⣝⢶⠛⠈⣇⣿⢸⣇⣿⣿⣿⣿⡟⠸⣹⠁⣿⠏⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠁⡞⣠⠀⠀⠀⠀⠀⠀⡎⢋⠞⣤⣧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⠀⣄⣷⣙⢯⠻⡌⣷⣿⣿⢻⡇⣿⣿⣿⣿⣿⢹⡆⣿⢸⣿⣿⣿⣿⣿⣿⠀ ⠘⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⡇⢶⡁⢴⠀⡇⠈⠀⠀⠀⠀⠁⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣆⡙⣿⣿⠹⣄⣷⣿⡈⣿⣿⣿⣿⣿⣿⠘⣷⣿⣇⣿⣿⣿⣿⣿⠀ ⢀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣽⣉⠸⠀⡀⣧⠉⠛⠶⠤⣺⠉⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢿⠙⣄⢷⣏⣿⣿⣿⣿⣿⢹⡄⣿⡇⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣸⠐⠀⠀⡀⠀⠀⠀⠀⢹⣇⣀⣧⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢷⣎⣿⣽⣿⠙⣀⣦⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠀ ⢛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣏⡖⠿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⢦⡝⣿⣹⣷⢿⠻⡈⣦⣿⣿⣿⢿⡀⣷⣿⣿⣿⣿⢸⠀ ⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⠻⠀⠀⠀⠀⠀⠁⠟⣿⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣄⡼⣿⠙⣧⣿⣿⠻⡈⣦⣿⣿⢹⡄⣿⣿⣿⣿⣿⠀ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⢤⠤⡤⣤⣥⣩⢚⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⡝⣷⠘⡄⣿⣿⣿⠻⡌⣷⣿⠘⣇⣿⣿⣿⣿⠋ ⣿⣿⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠤⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣹⣄⠤⠀⠀⡇⣮⡹⢹⠀⡄⣿⣿⣿⣿⠹⣶⣿⡘⣧⣿⣿⣿⣿ ⣷⣿⢻⠀⠀⠀⢄⠓⡍⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢀⠈⠀⠀⡇⢀⣄⡿⠸⠄⡈⣷⣿⣿⣿⣿⣽⣿⡈⣧⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⣄⣷⠻⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠢⣿⠛⠚⠙⡄⡿⠀⠀⡆⢹⠀⣄⡙⣧⣿⣿⣿⣿⡿⢿⠈⣷⣿⣿ ⣿⣿⣿⠸⠀⠀⠄⠋⣒⠙⡌⣶⡛⢮⠘⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⠴⣿⠉⠉⡔⢀⣸⠀⠀⠀⣇⠘⠀⣇⡹⣷⣿⣿⣿⣿⣿⢿⠀⣧⣿ ⣖⣿⣿⣿⠀⠀⠉⡂⣕⠬⠲⠒⣅⣿⣸⢦⡿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠖⠷⣽⣠⣀⡆⡘⢀⠀⠀⢼⡇⠙⠀⡀⢻⠀⠀⣧⡼⣿⣿⣿⣿⣿⣿⢻⠀⣿ ⠈⣿⣿⣿⠀⠀⠀⣽⣤⡣⣟⠿⠛⡙⣯⠽⡰⣧⢼⠒⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⣴⣀⣀⣄⣧⠻⢿⠀⠀⠀⢸⡄⣦⢿⠻⣿⠈⠀⡀⣷⣌⡻⣿⣿⣿⣿⣿⠘⡟ ⠸⣿⣿⣿⠀⠀⠈⣄⠤⢀⠀⠁⠞⠶⠶⡓⢿⠐⣖⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣾⣶⣿⣿⣿⣩⠀⠀⡇⢸⠁⠃⣿⣿⣿⢿⠛⠉⡄⢻⣆⡎⣤⣿⣿⣿⢹⡇ ⢹⣿⣿⣿⠁⡟⢸⠀⠀⠀⠏⣻⠛⠛⠉⠋⣞⢿⠹⣆⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠙⡆⢿⣿⣿⢹⠛⡉⣿⣿⣿⢻⠀⡇⢹⠟⣿⣿⣾⣧⣿⣈⣀⣄⣧⢻⢸⠀⡷⣿⣿⣿⡆ ⣧⣏⣿⣿⡟⣿⢈⠀⠀⡇⣿⣿⣾⢀⣄⣷⣿⣿⣟⢹⡄⣷⢿⠈⠀⠀⠀⠀⠀⠀⡄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣍⣟⣶⢲⠙⡏⣿⢹⠀⠀⡄⣿⠈⠀⡇⣿⣿⣿⢸ ⠚⣷⣿⣿⣿⣿⢿⠙⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢹⠀⢷⣌⠳⠀⠀⠀⠀⠀⠀⠂⠉⠤⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿⣺⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⣿⢹⠇⡇⣿⣿⣾⢿ ⠀⠀⣧⣿⡋⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣾⣴⢀⡆⢸⣷⠹⠷⢀⡀⢧⠘⠀⠀⠀⠀⠀⡀⣄⠶⠲⠒⠒⠒⠒⠶⠶⠤⣠⣇⡘⢠⠀⠀⠀⠃⢸⣿⣿⠘⠃⠀⣇⣮⠇⡀⣿⣿⢿⣿ ⠀⠀⠀⣷⣸⠀⠓⡙⣿⣿⣾⣿⣽⣩⢉⠛⠟⣹⠈⢇⡂⣾⡘⢷⠚⠀⣆⠙⠀⠁⠖⠠⠞⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠀⠀⠀⠀⡇⢀⣿⣿⢸⡇⠁⡇⢸⡧⠈⣧⣿⣿⣿ ⢅⠙⠀⡄⢿⠀⠀⡆⣠⠀⣀⣀⠀⠀⠀⠀⠀⠀⣄⣷⢸⣆⣧⡄⢿⠘⠀⣆⠿⢠⠀⠀⠀⠀⠀⠁⠋⠚⠔⠀⠀⠀⠀⠀⠀⡇⠙⠀⠀⠀⣸⠀⣿⣿⢸⡀⡇⡇⢸⡇⢸⡇⣿⣿⣼ ⡼⣷⠘⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣦⠹⢻⣇⢿⠌⠿⡌⠹⠀⠀⠉⠋⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⡇⢸⠀⣿⣿⢸⠀⡇⡇⢸⡇⢸⡇⣿⣿⢹ ⢻⡀⣧⠈⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣯⡏⠘⣷⣿⡜⣿⡞⠿⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠸⡇⠀⠀⣿⣿⢻⠰⡿⡇⢸⡟⢸⡇⣿⣿⡄ ⡦⢻⠀⢷⠈⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⣿⢹⡆⣿⣿⣯⢿⡎⠸⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠳⠈⠀⡇⢸⠀⢰⢸⠀⠇⣿⣿⢿⠀⣼⡇⢇⣿⢸⡇⣿⢰⠀ ⠻⣿⠹⡄⢿⡈⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣷⣿⠈⣿⣿⣹⣷⢻⣦⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⠈⡇⣿⠀⡇⢰⠀⡟⣿⣿⢸⠀⠸⣿⡏⣿⢀⡏⣾⠀⡷ ⣧⠸⣧⠙⡆⢿⠈⠣⢧⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣧⡈⣾⢸⣷⣿⣿⡏⣿⢹⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⢸⡇⣿⠀⡇⠀⠁⣿⣿⣿⢀⠀⢸⠀⣿⣿⠀⣿⢠⠀⡟ ⠀⣧⣝⣿⠘⣇⣿⠙⠻⣆⠙⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⢹⢧⢿⡇⣿⣿⣼⣿⣿⠸⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡿⡆⠀⡄⠀⡇⣿⣿⣸⠀⡇⢸⡏⣿⢸⡏⢸⠀⡏⣿ ⢧⠈⣄⣷⣿⠙⣦⣿⣿⠹⣏⠻⡴⢟⠿⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣿⡘⣿⣿⣿⡟⣿⣿⡄⢿⠈⠃⠀⠀⠀⠀⠀⠀⠄⠹⡆⠸⠀⠀⠀⡇⣿⣿⢀⠀⡟⠁⣿⣿⢰⡄⠁⢿⣠⠉ ⠙⣦⠙⡀⣧⣿⢻⣎⣿⣿⣿⣼⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣇⢸⣿⣿⣿⣸⣿⣿⠹⡇⢿⡙⢷⠀⠀⠀⠀⠀⠀⣧⢻⢻⠀⠀⠁⣿⣿⣼⠀⠇⣻⡿⣿⣼⠀⠀⡿⢛⡿⣿ ⡀⣤⡷⠻⠀⣆⣿⣿⡟⣿⣸⡟⣿⣿⣼⢀⠀⠀⠉⠛⠐⠋⡼⣇⢷⡄⢿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⢿⢻⠃⠛⠛⠬⠿⡿⣿⣿⠀⠀⡟⣿⣾⠀⠁⣿⣿⣿⣿⢀⠁⡿⣿⣴⣇⢀ ⠀⠀⠀⣀⣦⡿⡻⣾⣿⣿⣏⣿⣿⣴⣏⣿⣿⣷⣯⢖⡿⣿⣿⡿⡇⢸⣿⣿⣿⣿⣿⣾⣿⣿⢸⣇⣿⣿⣿⢻⣮⣿⣿⣾⣷⣿⣿⠀⡆⣯⣾⢠⠀⡿⣿⣿⣾⢁⠟⣴⣀⣾⠀⡼⠃ ⠀⠀⠀⠀⠀⡂⢶⣿⣿⣿⣷⣿⢻⡿⣿⣫⢟⣿⢛⠉⠈⡀⠀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣸⣿⣿⡻⣝⣳⣦⢿⠉⣿⣷⠀⠇⣾⢠⠁⡿⣿⣿⣽⢟⣴⢀⠀⠇⢰⠇⢠⡞ ⠀⠀⠀⠀⠂⠀⠀⡞⣦⡛⡟⣿⣿⢞⣷⣿⣿⣿⣿⣿⣿⣿⠿⡿⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢷⡄⣷⣿⣿⣼⣤⣷⣿⣿⡟⠁⣾⢀⠋⡿⣿⣿⣿⣴⢀⠀⠀⠀⡞⠀⡾⠇⢸ ⠀⠀⠀⠀⠀⠀⡰⠀⠀⡀⣬⣣⣴⣶⠷⡛⣯⣵⣿⣿⣿⣿⣿⣿⢻⡉⣯⣷⣿⣿⣿⣿⣿⣿⣿⢸⡄⠰⡀⣄⣦⣿⠉⠀⣧⢹⣾⣴⢁⠟⣾⣵⣞⣿⢀⠀⠀⠀⠀⠇⢸⠃⢠⡄⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠁⣾⠏⣿⣧⡎⠹⠀⠀⠀⣄⢳⠈⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⠘⠀⠀⠀⡀⢻⣼⡇⠀⢻⣦⠘⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⢄⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢋⡰⠀⠀⠀⠀⡇⣇⢰⡿⢹⣧⡇⢠⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⣄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢣⢰⠀⠀⠀⠀⠀⡄⡿⠀⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠛⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⣸⠀⠀⠀⠀⠀⠀⠀⣾⠇⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡀⢷⡌⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⡀⢸⡆⣿⣿⣾⣼⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⣀⢄⠦⠲⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣵⢿⢠⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣸⡇⣾⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⢸⡿⢉⠉⠀⠀⠀⠀⠀⠀⡇⠘⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⠉⠛⠾⠀⣳⢻⣾⣉⣉⣿⠴⠀⠀⠀⠀⠀⣆⠹⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠂⠖⡦⣭⣭⣫⣚⠀⡄⣿⢳⠟⢹⠉⠉⠀⠀⠀⠀⠀⠀⡀⢤⣾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⣀⠀⠀⠀⠀⠀⠀⠏⡬⣉⣟⣶⣡⠉⠀⠤⣤⣂⢖⣤⡀⣶⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢲⠙⠈⠀⠀⠀⠀⠀⠀⣧⣦⣤⠤⣡⣉⠀⠀⠁⣾⠲⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠴⣠⣍⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⡀⣄⠤⠢⠒⠙⠉⡌⣢⠒⣐⠀⠀⠀⠂⠐⠀⠉⠊⡐⣀⣤⠤⠺⠓⠉⠚⠖⠥⣨⢀⠀⢤⣀⢀⠀⡀⢄⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠞⣤⠳⠈⠀⠀⠀⠀⠀⠐⠀⠀⠁⠋⡴⣀⢖⠤⠦⠶⠵⠋⠛⠛⠴⣤⢤⠦⣶⣶⢿⠙⠈⠀⠀⠀⡀⣀⣄⠠⠀⠉⠚⠖⣦⣒⡀⢤⠑⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠟⣻⠶⡴⣀⢒⠄⠀⠀⠀⠀⠁⠋⠿⣠⠀⠉⠋⠀⣀⣀⢁⣽⢀⠀⡄⠻⠀⠀⠀⠀⠀⡄⣿⣾⢧⠾⠻⠛⠛⠛⠛⡽⢁⠉⠛⠛⠘⠀⠉⣉⣄⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠞⣤⢤⣤⢬⠀⠀⠉⠉⠋⠚⠶⡤⣠⣿⢛⡿⣴⢀⠁⠉⠀⠀⡟⣿⣟⢿⣿⣿⢹⠀⠀⠀⠀⠀⡄⢿⡿⢰⠀⠀⠈⠇⣿⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀ ⠀⠀⠋⡿⢿⣿⣿⣿⣛⣉⣀⣀⣀⠀⠀⠀⠀⠀⣷⣿⢡⠟⣴⢀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⣇⣿⠹⠀⠀⢃⣾⢡⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠋⠙⠀⠀⠀⣧⢿⣿⣰⠀⠀⠀⠀⠀⠀⡀⣧⣬⣭⣺⣰⠀⠀⠉⠞⠠⠈⣿⣿⣿⠀⠏⣼⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢳⠈⠀⡇⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠛⡅⢀⠉⠋⡿⣿⣿⣼⡟⣿⣧⡽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⠹⡏⣸⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⢢⡼⣭⣿⣼⣧⣿⣼⠃⣾⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣧⣿⢿⣿⣿⣿⣭⣿⠿⠷⣿⢉⠉⠉⠈⠀⠀⣿⢀⠀⢻⣿⣼⠁⡇⢿⢰⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡄⢻⠀⣆⣿⣿⣿⣼⠸⣆⣈⣇⣈⣀⠀⠄⢠⠀⠀⣿⠀⠃⣿⣿⢸⡞⡄⢸⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣇⡌⠘⣇⣆⣿⣿⣇⢧⢧⠈⣆⠙⠀⠀⠁⠛⠿⣿⠿⣿⣿⣿⢸⢠⠀⢸⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⡀⢳⣆⠙⢧⣆⣿⡈⢹⢻⣿⠻⣟⢿⡷⣿⣿⣿⣿⣿⣿⣿⢹⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀ ⠉⠒⠁⠈⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠋⠛⠉⠿⠿⡷⣿⢣⣷⣼⢐⠀⠀⠀⠀ ⣷⠿⠻⠉⣀⣢⣁⣀⣅⢠⠀⠀⡀⣘⠀⢄⠋⣿⣺⣵⣾⣴⣤⢀⠀⠁⠔⢀⠉ ⡄⢦⠝⣟⣼⠿⠈⢆⣨⠀⠀⠁⠔⢄⠢⠓⣿⣿⠀⠰⠑⠀⠀⠓⡺⠒⠖⡤⢀ ⠀⠀⡀⣀⣮⣷⢿⠉⡀⠢⠑⠀⠀⠀⡰⣁⣿⢿⡠⠀⠀⠘⠀⡂⣿⠈⠀⠀⠀ ⠀⠊⠛⢺⠀⢁⣽⣷⣿⡿⢿⡹⠹⠈⠂⡏⣿⢰⠀⠀⠀⢀⠀⠀⡧⢻⠀⠀⠀ ⠇⢠⣇⢁⠛⣾⢠⡟⣿⣿⣿⣹⣤⣷⠻⡟⣿⢸⠀⠀⠀⠀⠀⠀⡀⣿⠘⠀⠀ ⡆⢿⠻⢟⠿⣿⣷⣿⣿⣿⣳⣐⠀⠀⣧⣿⣿⠘⠀⠀⠀⠈⠀⠀⠀⡗⢸⠀⠀ ⠀⠀⣀⣀⣀⣀⣀⣯⣿⣿⣻⠞⠚⠀⡇⣿⣽⢨⠀⠀⠀⢱⠀⠀⠀⣿⢰⠀⠀ ⠀⠀⠀⠀⠀⠁⡭⣾⡬⣀⢀⣾⣤⢠⡀⣾⣿⢻⠀⠀⠀⠑⢔⠀⠄⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡼⢳⢸⠀⣿⠉⠊⠠⠀⣆⣽⢽⠀⠀⠀⡈⠀⠁⠟⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⡴⣷⠿⠈⡀⠀⠀⠀⠀⠀⣎⢻⠛⠒⠤⠂⠔⡠⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⠻⣿⡻⠹⠉⠉⠛⠗⡿⣯⢚⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠟⣿⣿⣿⣿⣿⣿⣿⡀⣷⣿⢿⠛⢯⠹⠸⠿⡏⠶⢶⠘⠀⠋⠒⠟⢈⠀⠀⡟⠖⡤⣋⣴⣀⢁⠈⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣾⣶⣤⣡⢘⠀⡟⣿⣿⣿⣿⣿⢿⡴⣯⠴⣤⣶⠘⢷⠈⠀⣄⠻⠁⢺⠴⣠⢄⠠⠞⢀⡀⠱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⣀⠀⠀⠁⠟⣿⠐⠏⣶⣤⣀⢀⠀⠀⡆⠙⠦⠈⠀⠀⡄⣿⢷⠘⠀⡇⣸⠀⠀⠀⠊⡷⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠁⠀⠉⠄⣤⣁⠊⡴⢀⠀⠀⠀⠀⠀⠀⠀⡏⠻⢟⠾⠤⠦⡼⠀⠀⠀⡇⢷⠛⠖⡠⢀⠀⠀⠋⡶⢘⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠛⡾⣤⢤⠤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣷⢸⡀⢦⡗⢨⠀⠀⠔⢋⡰⠀⠀⠀⠀⠋⡰⠀⠀⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡘⠀⠀⠀⡏⣿⠿⠼⡾⢀⠀⠁⠊⠴⣠⠀⠀⠀⠃⣰⠀ ⠙⠈⠀⠀⠁⠉⠛⡴⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠛⠿⣿⣿⣿⣿⢀⠀⠁⡸⠀⠀⠀⠀⠃⡽⢀⠀⠀ ⣿⣷⣿⣿⣿⣴⢁⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣠⡀⠢⠓⡟⠘⠀⠀⠁⠟⣼⣀⢳⠀⠀ ⢋⡿⣿⣿⣼⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠄⡠⢀⡜⠀⠀⡇⠀⠀ ⣿⣿⣿⣿⠋⠟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⠓⡴⠀⠀⠇⣧⣀⠀ ⣿⣿⣶⣠⢋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠋⡴ ⣹⢀⠁⠞⢠⠀⠀⠀⠈⠀⠍⠾⡶⢙⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠓⠋⠒⠴⣷⣼⠀ ⠠⠋⡴⢀⠀⠁⠋⡴⣠⢀⠉⠛⠞⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀ ⠏⢢⠒⠶⡿⣿⢻⠙⠉⡟⣼⠠⡷⣯⣿⣿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀ ⢀⠀⠋⠐⡓⣍⣯⣿⣿⣿⣿⠿⣿⣙⣯⣿⣿⣿⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠤⠀⠉⠀⠀⡇⢿⠙ ⠟⡴⢀⠀⠀⠀⠀⡀⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⡶⣶⣶⣻⠙⣿⣿⣿ ⣰⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⡀⣀⠤⣦⣒⣲⣓⣉⠛⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠶⠷⠚⠛⣙⣄⠳⠈⠀⡏⣜⣧⣿⣿ ⠀⠀⠀⠀⣄⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⢿⡿⣯⠻⠀⣆⠘⡇⢹⠀⣆⣿ ⢸⠀⠀⠀⠀⠀⣄⢷⠻⠉⠀⠀⠀⠀⠀⠀⠉⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡙⣷⣿⢻⡟⣿⣿⣿⠘⠀⣿⢈⡇⠀⠀⣧ ⢸⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⠿⠛⠙⠋⠿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠱⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⡇ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣶⢶⠶⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠤⣒⣤⣶⣤⣧⣿⣬⣿⢿⠙⡆ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⢸⡀⣸⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠒⠤⠤⠤⣀⣏⣶⣠⢀⠀⠁⠋⠼⢃⠳⠀⠀⠀⠂⠷⠻⡿⢿⠙⠉⠀⠀⠀⠀⠁⠉⡏⠙⡆⢹⠉⢸⠀ ⢸⠀⠀⠀⠀⠉⠒⠴⣀⢀⠀⠀⠀⠀⠋⠞⣠⢀⠁⠊⠔⡠⢁⡰⠋⣰⠀⢣⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣤⣤⣠⣀⣀⣏⣀⠀⣷⠇⢸⠀ ⢐⠀⠋⠾⣠⠀⠀⠀⠀⠀⠀⠀⠋⡼⣀⠉⠖⡠⢀⠀⠀⠁⡱⡟⣸⠀⠀⠀⢳⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢰⠀⠀⡇⡟⢀⠀ ⠞⡠⣠⠀⠀⠀⠀⠀⠀⠀⠁⡾⣡⠞⡠⢀⠀⠀⠀⠀⠃⡿⣱⣿⢼⠀⠀⠀⡇⠘⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⠀⠀⠀⡏⣸⠀⠏ ⢠⠀⠀⣀⠤⠲⠙⠀⠁⠟⣿⢔⣀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣀⣾⠀⠀⠀⡇⢻⡞⣆⠘⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠄⠀⠀⣾⠀⡄⢀ ⠀⠀⠀⠀⠀⠀⣤⢦⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠃⣽⡟⣷⡿⢦⣓⠻⠀⠀⡃⣿⢸⠀⢳⠀⠁⢿⠀⠀⠀⠇⣿⢠⠀⠀⠀⡏⢠⠀⠋⠴ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠋⠞⡷⡞⢠⡹⣸⠀⠀⠀⠀⠀⡇⣿⢀⠀⡇⠀⡜⠀⢸⠀⠋⣴⢠⠀⠀⠉⠚⢴⠤⣤⣀⣤

⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠿⠻⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠙⡄⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠁⠔⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⡇⠀⢳⠈⠁⠚⠓⠈⠀⠀⠀⠀⠀⠀⡆⠘⠁⠞⢀⠀⠀⠀⠁⠊⡴⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣈⠦⠑⠈⠀⠀⠀⡇⠀⠈⣇⣸⠀⠸⡀⢦⠙⠀⠀⠀⠀⠀⣧⢁⠉⠉⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣼⢣⠀⠀⣀⠤⠓⠈⡇⠀⠟⣼⠀⠉⢻⠛⠙⡈⢦⠘⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠟⢴⠀⠁⡎⣶⡴⢤⣤⣤⢶⠓⡉⣧⠛⣿⣾⣤⣀⣀⣀⣀⣀⣀⣤⠲⠙⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⢀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠑⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⡀⢣⡈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⠀⠀⠀⠀⠀⠀⢹⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⡇⠐⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⣷⢿⠼⠶⠈⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠤⡒⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⡀⣧⢿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣿⠙⠀⣆⢹⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⣹⠋⠀⠀⢄⠢⠑⠈⡀⢠⠀⠀⠀⠀⠀⠀⡀⢯⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡶⣴⣠⠀⠀⠀⠀⠀⣀⢄⠤⣒⠒⠁⠉⠉⠟⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣼⣷⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣴⣁⣿⢿⠺⠁⠉⠉⠀⠀⠀⠀⠁⡟⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣶⣭⣉⣉⣍⣧⢻⠀⠁⡜⣠⣖⠤⡤⣤⢢⠑⣌⠣⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⢁⡞⣄⣡⢋⠿⣶⡤⣤⣤⠧⣰⠀⠍⣉⣍⢾⠶⠤⡧⣤⠹⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠟⣾⣡⠈⠄⠤⠤⠀⡄⣠⣀⠀⠲⠀⠀⠀⠃⣽⠉⡉⣻⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠊⠤⠤⠒⠉⠈⠀⠀⠀⠂⢻⡴⣾⣤⢀⣏⠙⠈⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⠾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⡠⠀⠀⠛⠈⡀⠱⠀⠀⠀⠀⠁⡟⢸⠀⡄⣷⣶⢷⠘⠏⣿⡿⣿⣿⠻⢚⠀⠀⠀⠀⠀⠖⡷⣿⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣸⠀⠀⡿⣿⢻⠙⡀⠸⠀⠀⠀⡟⣿⠀⠀⠀⡀⠳⡀⣦⣿⣿⣿⣿⠛⣟⣿⠘⠀⠀⠀⠀⠀⠀⠀⣀⢄⠲⠉⠀⠀ ⠀⠀⠀⠀⠀⢦⠘⡄⣶⣿⣿⣴⠁⡜⠀⠀⠇⢰⣇⠀⠀⠀⠀⡀⢦⠈⠀⣄⣦⣒⣉⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⢯⠘ ⠀⠀⠀⠀⠀⠀⡄⠲⠉⡀⢠⠊⣠⠀⠀⠀⡇⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⣀⣄⠤⠷⠈⠀⠀⠀⠿⣀⣀⣀⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⡄⢹⡄⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⢣⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⣌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠅⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⠊⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠒⠒⠙⠒⠒⠒⠤⡠⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣄⣀⣴⣿⣿⠟⠁⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠉⠉⠉⠙⠻⢿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣦⣄⡀⠀⠀⣀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣾⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠋⠀⠀⣠⣾⣿⣿⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠁⠀⢀⣤⣶⣶⣶⣦⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿ ⣿⣿⣿⣿⠇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣄⠀⠀⠙⠻⢿⣿⣿⠿⠟⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⣆⠘⠀⠀⠁⠛⠰⠀⠀⠀⠀⠋⠚⡶⣷⣿⣿⣿⣿⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⢧⠈⠀⠀⠀⠀⠀⠁⠞⣴⢀⠀⠀⡀⣷⣿⣿⣿⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⡛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⡀⢷⠈⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⠤ ⠀⠃⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠟⡴⣠⢀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡄⢻⠈⠀⠁⣼⠀⠀⠀⠀⠀⠀⠉⠟⡶⣤⣀⠀⠀ ⠀⡆⠈⣄⠦⠙⡄⣷⣿⣬⣤⣀⣀⣀⢁⠋⠚⠄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣆⣼⢧⡿⠛⠸⠁⠋⠛⠴⣤⣉⠚⠴⣤⢀⠀⠀ ⠀⠀⢷⠙⠀⡀⢤⡶⣘⢦⠓⠉⠈⠀⡠⢀⠁⠉⠛⠛⠞⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⣇⠉⣾⣠⢀⠉⠖⡤⢀⠀⠀⠀⠀⠀⠀ ⠉⠋⡚⣶⠶⠒⠒⠀⠁⠉⠛⡴⣥⣯⣴⣤⣀⣀⣀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡏⣰⠉⠚⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣗⠛⠉⠀⠀⠀⠉⠛⡴⣀⠁⠟⣴⠀⠀⡄⢤⠶⠙⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣸⡄⣀⠀⠀⠀⠀⠀⠀⠉⠚⡴⣻⢀⠀ ⠀⠀⣋⣙⣈⣀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠋⠐⢧⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⢸⠀⠀⠂⠴⢡⠋⠞⡤⣀⠀⠀⡇⠀⠀ ⠀⠇⢀⠀⣆⠾⠒⡛⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠞⢠⠀⠀⢦⡜⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⠀⠇⢠⡀⢲⠋⠛⠿⡽⣪⢖⠤⠤⠤⠶⠙⡇⠀⠀ ⠀⡼⠀⠀⠀⠀⠀⡟⣤⠱⠈⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⣄⡳⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠀⠀⠃⣸⠁⠋⠛⡿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀ ⡆⣿⠿⠸⠀⠀⠀⣧⠈⠀⣄⠦⠓⠉⠀⠀⠉⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀⠁⠟⣶⣤⣋⡾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀ ⠀⣇⣿⢠⠀⢦⠙⡇⢠⠀⠀⠀⠀⡀⣀⢤⡶⠙⠀⠀⠀⠀⠀⠀⠀⠁⠛⠞⣶⣶⠶⠙⠈⠀⠀⠀⠀⠀⠀⠖⣠⢁⠋⠞⣠⢀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢀⠀⠀ ⠇⡀⢀⠄⠀⠃⣄⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣳⠙⠀⠾⠶⡤⣀⠀⠀⠀⠁⠞⣤⣳⣦⣤⢶⡽⣭⣭⣬⣤⣦⣳⠈⠀⠇⣠⠀⠀⠀⠀⠀⠀⠁⠞⣤⣁⠐⠀⠃⣾⢀⠀⠀⠀ ⡀⢿⠘⠀⠀⡀⢣⠉⢿⠉⠉⠀⠀⠀⠂⠙⠀⠀⠀⠀⣤⢻⠀⠀⠀⠀⠀⠁⠟⣼⢀⠀⡀⣦⠷⠻⡈⣀⠀⣀⢦⠙⠀⡀⢦⡘⠀⠀⠀⠀⠀⠀⠀⣠⠁⠞⣠⠁⠎⣷⠀⠀⠀⠀⠀ ⠀⣇⢹⠀⠀⠀⠀⣀⠀⠀⣇⢿⠈⠀⠀⣇⠻⠉⠉⠋⡼⢀⠀⠁⠉⠛⡿⣿⣰⠀⠀⠀⠀⠀⠀⣄⢹⠀⠀⠀⠀⡀⢦⠙⠀⣄⢦⠳⠉⠀⠀⠀⠀⠁⣋⠛⠿⣠⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⣾⠳⠈⠃⠉⠉⠚⠲⡗⣼⣀⢤⠶⣠⠀⠀⡞⣀⣀⣀⣆⣘⣀⣆⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⠀⠀⠀⡀⣄⠲⠒⠛⡉⣉⣉⣋⣒⣖⡤⣀⠀⠀⠀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣶⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠈⠀⠀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀

⠀⠁⠀⠀⡇⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⡋⣸⡀⠀⠀⠟⣠⢀⠀⠀⠀⠀⠀⡀⣷⣻⣟⣙⣼⣀⢳⣇⡉⣄⣳⣮⠘⠀⠀⠀⠀⠇⣦⢸⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠠⠀⠀⠀⠀ ⠀⣤⠀⠀⡜⠀⡇⣼⠀⠀⠀⠀⠀⠀⠋⡞⣶⠀⠆⠉⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⠀⣀⣄⠠⡄⠻⣛⢿⠛⣌⣝⠙⠀⠀⠀⡟⠀⢻⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠄⠀⠀⠀⠀ ⠀⡇⠀⠇⢠⠀⡇⢸⠀⠀⠀⠀⠋⡶⣠⠀⠀⡄⠣⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⣤⣳⣿⡟⣬⠹⠀⠀⣿⠀⡆⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⠀⡴⠀⠀⡿⢀⠀⠁⠊⡴⢀⠀⠀⠀⡧⡿⢟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣿⠹⠀⣧⠀⠀⣧⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀ ⠀⢰⠈⠀⠀⠏⢰⠁⠞⣠⠀⠀⠀⠀⠀⠃⣸⣀⢷⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⡏⠀⠀⠀⢧⠈⠀⠀⠀⠀⢸⠀⠀⠀⢠⠊⠾⣠ ⠀⠜⢀⠀⠃⣿⠞⣠⠀⠀⠀⠀⢀⠀⠀⡏⢀⠀⡇⠹⠀⠀⠀⠀⡁⢀⠀⠀⠀⠀⠟⢠⣿⠀⠀⠀⠀⡀⣤⠠⠀⠉⠉⠀⠀⠀⡀⣧⠸⠀⠀⡀⣳⢦⠙⠀⠇⢸⠀⠀⠀⠀⡜⠀⠀ ⠜⠀⠀⠁⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣦⣶⢴⣤⣤⣀⣀⣤⢤⠤⣥⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⠯⠛⠈⠀⣧⠘⠀⠀⡀⢷⡈⢷⡏⠀⠀⠀⠀⠁⢀⠀⠀ ⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡅⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣝⠦⡙⣿⠘⠁⠀⡀⢷⡎⣿⠀⠀⠀⠀⡌⠀⠀⠀ ⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⡤⣧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⣄⢦⡐⣤⣿⠈⢷⠈⠀⣧⣿⠀⠀⠀⠀⢸⠀⠀⠉ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣰⣦⠛⠛⠛⠛⠞⠴⡤⣁⣛⣖⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⣠⠀⠀⠀⠀⠀⠈⡀⢧⠙⢷⠘⡇⣸⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠲⠒⠛⠚⠓⠒⠒⠤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣋⠠⠀⠀⠀⠀⠀⠀⡄⠹⠀⣄⣷⣿⡿⢀⠀⠀⠀⠀⣸⠀⠁⠠ ⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡾⣶⡠⢀⠀⠀⠀⠀⠀⡷⠻⠙⣍⢳⠈⡀⣧⣽⠀⠀⠀⠀⠀⢀⠀⡄⠀ ⠇⣿⢸⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⡀⣦⣿⡿⣯⢿⠀⠀⣿⠀⠀⠀⠋⠠⠀⠄⠀⠀ ⣧⣿⢻⠄⡀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣶⡤⣤⣦⢷⠛⠈⠀⠀⠀⡀⣶⢾⣿⢻⠀⡆⢸⠀⠀⢠⡀⠘⠀⠀⢣ ⣧⣴⢀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣴⢋⡴⣄⠦⠓⠉⣆⢻⠘⠀⠀⠀⠀⣇⣽⣿⢹⠀⢣⠀⠀⠀⠂⠀⠀⠀⡆ ⡌⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠻⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⣸⠀⠀⠀⠀⣄⠿⣿⢸⠀⠀⠀⠀⡇⣻⣻⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢰⠃⠿⠠⠀⠀⠀⠃⡿⣠⢁⠚⠛⠉⣀⣦⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⢹⠈⠋⠿⠛⠟⣿⣿⢠⠀⠀⠀⠛⡽⣿⣿⣾⢸⠀⠀⠀⠀⠀⠸⠀⠃⠀ ⠀⠀⡇⠘⡿⣾⠀⠀⠀⠀⡇⢻⡿⡾⠀⠀⡀⢦⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⡀⣦⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠋⡿⣿⣿⣾⣡⠟⣾⠀⠀⠀⠀⠀⡀⢜⡀⠀ ⠀⠀⡇⢿⣿⢸⠀⠀⠀⠀⡇⢿⣿⢸⠀⠁⠉⠀⡏⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⠻⡛⣝⣿⣮⣶⣠⢉⠋⠟⡿⣿⣽⢋⣿⢓⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠦⠘ ⠀⠀⡇⣿⣿⢸⠀⠀⠀⠀⡄⣿⣿⣿⠿⣿⣿⣿⣿⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⡾⣓⣻⣯⣿⣿⣿⣻⣟⣿⣿⣾⣶⣿⣙⣏⢀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠀⡄⣿⣿⣿⣼⢤⡿⠀⠀⠀⣄⣶⣿⣿⣿⣿⣾⣫⡾⢱⠛⠟⠋⠓⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣤⣷⣿⣿⣼⣷⠞⠤⣀⡇⡈⣴⠀⠀⣿⠀⠀⠀⠀⠠⠄⠒⠉⡇ ⠀⠀⠀⣿⣿⣿⢸⠀⣿⠉⠉⠉⠛⠒⠖⣷⣿⠿⡿⣵⢞⣫⣰⣆⢰⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⠤⢹⠀⣧⡟⢸⠀⣆⠹⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⣇ ⠀⠀⠀⡆⣻⣏⠀⠀⣿⣿⣿⣿⢰⠀⠀⡟⣿⣿⣶⣠⠃⣼⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⣷⢀⠀⠀⣆⠸⠀⢸⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⣿⣆⢸⠀⣧⣍⣧⣼⠀⠀⠀⣽⣀⢀⠁⠛⡼⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⠀⠀⠀⠸⣧⠉⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠹⢸⠀⡇⣸⣇⢀⠀⠀⠀⣼⣤⡤⣀⠇⢸⠀⠀⠀⠀⡏⢀⠀⠀⠃⡷⢰⠀⠀⠀⠀⠀⠉⠈⠀⠀⡆⠸⠀⠀⠀⠀⠉⣿⣯⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⠲⠘⠀⠀⣧⢸⠀⠀⢳⡾⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠇⠠⠀⣿⠀⠀⠃⣴⣿⠀⠀⠀⠀⠀⠀⡄⣂⢷⠽⡯⢺⠒⠷⠿⣲⢤⣷⡀⣿⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢦⠙⠀⣧⠈⠀⡆⢿⠀⠀⢸⠀⢸⠀⠀⠀⡇⢸⠀⣸⠀⠀⢸⠀⠃⣰⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⣟⠀⣾⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⡀⣷⡻⢰⠀⠀⣇⠘⠀⢸⠀⢧⠓⠛⠞⡷⣸⠀⢸⠀⠀⢸⠁⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⢰⠀⠀⠀⡞⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀ ⣆⠹⠀⠀⠀⠀⣀⢧⠈⠀⠀⢀⠀⣧⠀⡇⠘⠀⠀⡆⢸⡇⢨⠀⠀⢹⡏⢠⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣞⠢⠈⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠃ ⠝⡄⢱⠀⠀⠀⠀⠀⣦⠻⠀⠀⠀⡇⠀⡀⢻⠀⠀⠀⢸⡇⢸⠀⡇⣿⣸⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢽⠋⢰⠀⡀⠦⢹⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠸ ⡹⢦⡜⠻⠀⠀⠀⠀⠀⣄⢷⠈⠀⠀⢻⠀⣆⠘⠀⠀⡇⠁⢸⠀⡇⣿⢠⠀⡇⢸⠀⠈⠀⠀⠀⠀⠉⠀⠁⠋⠛⣿⣹⣼⠀⠀⠀⠃⡀⢤⠳⠈⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡟⢰ ⡄⠘⡄⡷⢞⠘⠀⠀⠀⠀⡀⣦⠙⠀⡄⠘⠀⢳⠈⠀⡇⡌⢹⠀⡄⣿⠀⠀⡏⢿⡿⢟⠾⠉⠟⡴⣽⠞⣫⣿⢏⣿⣼⠀⠀⠀⠞⣠⢧⠈⠀⣀⢷⠉⠉⡞⢀⠀⠀⠀⠀⠀⡟⣾⠀

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⠀⠀⣢⣈⢀⠋⡨⠭⠼⠤⠦⠤⠤⠇⢿⠘⠈⠀⠥⠐ ⠀⠐⠈⠃⠀⣦⣤⣀⠁⠀⠀⢀⠐⡀⢦⠿⢐⠃⢀⠀ ⡂⢁⠩⣀⠐⠄⠁⠔⢀⠀⠀⠠⡀⠂⠈⠠⠀⠰⠀⠀ ⠀⠀⠇⠘⠚⠵⢭⠲⠁⠁⠊⠠⠉⠄⡁⠠⡰⠀⠀⠀ ⠀⠀⠀⣦⡓⠛⠞⠃⠀⡁⢌⠛⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠃⡟⡻⢽⠭⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⣤⡀⣀⣄⢻⠉⢋⢀⠁⠀⠈⠀ ⠀⠀⠀⠀⠃⡿⢠⡈⢀⠺⣴⣥⣷⠹⡉⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣝⣎⠁⡋⣛⢟⡴⣄⣇⢂⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢿⠻⣿⢰⣃⣿⠹⠏⣠⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⣶⣶⡶⣾⣷⣀⠳⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⠀⠀⣄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⠆⣠⣀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢁⠘⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠋⡰⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢡⠞⢀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠍⠫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢃⡼⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠔⣠⠋⠿⣾⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠁⡰⠀⠀⠀⠀⠊⡠⠀⠋⠰⠀⠀⠀⠀⠀⠁⠕⣾⣴⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡸⠀⠀⠀⠀⠀⠀⠁⠜⢀⠀⠀⠀⠀⠋⡿⣴⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡎⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠁⠀⠋⡞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⡎⢀⠀⠀⠀⠀⠋⡠⠁⠀⠁⠔⣫⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢷⠁⢰⠀⠀⠀⠁⡔⢀⠎⣡⠔⢋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⣸⡀⠀⠀⠀⠙⡼⠀⠑⠟⣾⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣎⠀⠀⠀⠁⡴⠀⠈⠋⡾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠀⠧⠤⡠⣄⣱⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣷⢱⠀⠁⠘⠀⠀⠁⡟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢱⠀⠀⡀⠀⣧⡻⢻⠀⠀⠀⠀⠀⠀⠀⡇⣸⡎⠀⡜⠀⠀⠏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠙⠉⠈⡄⠘⠀⠀⠀⡉⣻⣯⠿⠈⠀⠀⠀⠀⠀⣾⢇⢰⡏⢀⠁⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣷⣿⣿⣷⠹⠁⡿⣲⠙⠉⣛⣿⠻⠙⠉⠀⠋⢸⡘⠃⢠⠗⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⢡⠩⡟⣰⠀⠀⠏⣤⣤⠶⠁⡻⣿⣧⣿⢻⢉⡼⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢠⡄⣯⣰⠀⠀⠃⢠⠀⠀⠃⡤⣐⠀⠀⣇⢿⡼⢣⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠟⣸⠀⠀⠎⢠⠀⠀⠁⢰⠀⠀⣀⠀⡇⣿⢻⡿⣿⠘⠯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠈⠀⡴⠀⠀⠀⠀⡼⠀⠀⠁⠋⠿⣿⣶⣾⣤⣄⢲⡝⢻⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡞⠀⠀⠔⣧⣴⣠⢀⠀⡀⠀⠁⠋⣶⣂⢤⠻⠒⠒⠙⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⡏⢀⠀⠀⠏⢠⠀⠀⠀⠀⠉⠞⣠⢄⠀⠀⠀⡆⠙⠘⠋⣴⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⠀⠀⠀⠀⠀⠃⣿⢿⠻⠈⠀⠀⠞⢀⠀⠀⠀⠀⠇⣰⠈⠀⠀⠉⠊⠘⠀⠀⠀⢸⠀⢫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠹⣿⣾⣿⣼⢻⠈⠀⢠⠀⠀⠀⠀⠀⣺⡠⢃⠴⣀⢀⠀⡖⠈⠀⡆⠁⠴⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣿⣿⢿⣿⢸⡇⣿⣿⢿⠹⡀⠤⠀⠀⠁⠟⣶⣶⣵⢠⠀⠀⢇⠈⠃⢠⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠘⠈⠀⠀⣿⣿⣿⣟⣿⡇⣿⣿⣿⣿⣿⠿⠿⡿⣽⠲⠩⠛⠈⠀⠀⠀⠀⢄⡦⠙⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢦⣝⠐⠀⣾⣷⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣷⣿⣿⢷⣾⣧⣿⠸⠀⠀⠀⠀⠀⡀⢄⠳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⡋⢿⠿⢻⠙⣿⣿⣿⢻⣇⣿⣿⣿⣿⣿⣿⣿⣽⣯⢿⣿⣿⢿⠘⡇⢰⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣌⣷⣿⣿⣿⣿⣿⣿⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠏⣿⠽⣿⠚⡾⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⣶⠿⡛⣛⣝⣭⣭⢹⠂⠐⣧⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣻⢿⣿⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣋⣟⣿⠙⠂⠐⣷⣿⣿⠘⣯⣿⣿⣿⣿⣿⢂⣿⣿⣿⣿⠏⣿⣿⣿⣿⣟⣠⡟⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠟⣿⣽⣿⣴⣏⠿⠿⡿⣷⣿⣿⣿⣿⣘⣀⡀⢁⡞⣤⡿⣿⣿⣾⣷⣿⣶⣶⢶⡷⣽⢯⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣿⣿⣿⣵⢟⡿⣾⣠⢀⠀⠀⣄⣶⣿⣿⢿⠽⠈⣠⠉⠔⢀⣭⣚⠤⣠⢉⠚⠚⡭⣿⣿⣿⢹⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣻⠿⣿⣶⣱⠈⠀⠀⠀⠀⠀⠀⡀⣄⣿⣷⠿⡺⢖⠴⣠⢀⠀⠁⡉⢚⠴⣀⣄⠦⡙⣌⣦⠹⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣀⠀⠀⠀⣇⢼⠲⠉⠈⠀⠁⠋⠟⣼⢀⠀⣀⣀⠤⠤⠤⣰⣤⠀⠀⠀⠀⢸⠀⠀⢆⠜⡅⠹⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠌⠐⠀⠀⠀⠀ ⠀⠈⠐⠦⠠⠤⠤⡤⣤⣠⠐⠉⠈⠔⢀⠀⠡⠀⠀⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣘⠤⠂⠀⠀⠡⠀⠀ ⠀⠀⠤⠀⠀⠈⠄⠠⠀⠀⠀⠠⡄⢈⠀⠀⠢⡀⠐⠀ ⠀⠀⠀⠀⠁⢀⠀⢀⠀⠂⠀⠁⠛⠈⠀⠀⠀⢂⡄⠈ ⠀⠀⠀⠀⡘⡌⢀⠀⠀⠀⡰⠀⠄⢯⠀⠀⠀⠀⢡⠃ ⠀⠀⠀⠃⢠⢄⠀⡁⠀⠏⣿⠀⠀⣧⠀⠐⠀⠀⡀⡐ ⠀⠀⠀⣼⠠⠄⡠⣤⢤⠀⡿⠀⠀⠋⠀⠀⢄⠐⠈⠔ ⠀⠄⡄⢾⣿⣿⢶⠁⡿⢿⣿⠹⠀⢸⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⢋⣈⣀⣀⣀⢋⡖⢠⣾⠂⢀⠀⠀⠀⠀⠀⠀ ⡀⠀⢀⡀⡶⢩⠙⡭⠉⠋⠅⢰⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠀⠀⠀⠂⠀⠀⠀⠀⠀

⢡⠀⢀⠂⢀⠀⠀⠊⠀⠀⣶⣳⣿⣾⣷⣿⣮⣜⣤⣷⣿⣿⣿⠀⣁⢸⠟⣾⢺⠥ ⠀⠀⠔⢀⠁⠔⡠⠀⠁⠉⠉⠔⠂⡈⢀⣤⢷⡈⠻⠈⣆⣿⣿⣿⡿⣿⢧⣇⢿⣼ ⠀⠀⠀⠔⢀⠀⠀⡱⠔⠴⢀⠀⠀⡄⠘⠀⠀⣄⡵⣻⠧⣿⡇⣿⣿⠎⡿⣿⣿⢸ ⠠⠀⡀⠀⠀⠀⡇⣽⠀⢢⠒⠇⢉⠉⠠⠀⠀⠀⡀⣧⢿⣝⡷⣿⣿⢹⣷⣿⣿⢸ ⠘⠠⠀⠀⠀⠀⡇⢹⠀⠀⠀⡇⠶⢠⠀⠀⠀⠀⠀⡸⣆⣿⢧⡙⣦⣿⡜⣿⣿⢸ ⣿⠀⠀⠀⠀⠀⠀⣢⢥⠭⠦⣔⢀⠀⠀⠀⠀⠀⠀⠈⠀⣇⢻⣆⢿⡝⢿⣎⣿⢻ ⣿⠘⠀⠢⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠈⡀⣆⠈⣄⣿⣿⢫⣧⣿ ⣿⢸⠀⠇⡲⣮⠻⠟⠘⠀⠀⠀⠀⠀⠀⠀⠁⠊⠰⢺⡀⠠⠈⢁⡀⣟⣿⣿⢻⣧ ⡏⢻⠀⡢⣴⠥⡄⡹⢧⠀⠀⠀⠀⠀⠀⠃⡿⣚⣟⠿⠀⠸⣇⡿⠙⡆⣯⣷⣿⡟ ⣷⣿⡟⠀⠇⢿⠦⡿⢻⢦⠙⠀⠀⠀⠆⡿⣿⢿⣿⣿⠛⢽⣶⣩⢹⣀⢿⡄⣿⣹ ⡀⣿⣿⠿⡟⣿⣿⣶⣦⢻⣐⢢⠈⠀⠄⣢⣐⣀⣠⣒⣧⢠⠀⡄⣿⠀⡇⠀⣧⣿ ⠉⡄⠘⡆⣤⣤⠤⣀⠢⡘⣨⠹⢆⠜⢀⢀⠈⠒⠀⠀⠀⠈⠀⢸⣿⡀⡟⠇⡇⣿ ⣸⠰⢃⠀⠀⠀⠀⠀⠀⡦⣧⡎⡿⢼⠜⡀⠀⠀⠀⠈⠀⢸⠁⠀⣿⠀⣟⡏⡇⣼ ⡞⡌⠘⠣⠀⠀⠀⠀⠀⠀⡶⢸⣿⣿⢞⠀⠀⠀⢀⡀⠘⢸⠆⠇⣿⢀⡖⣼⡇⢇ ⡌⢿⡎⠻⢊⠉⠙⠀⠀⠀⠃⣧⣗⣿⢿⢡⠀⠀⠀⡀⢎⢸⠀⡇⣼⠇⡇⢺⢱⡞ ⠗⡘⣧⣟⢿⢿⣿⠀⠀⠀⠊⡸⡿⣿⣿⢸⢻⢹⠀⠉⡏⠘⠀⣿⢠⡿⣿⢁⡛⡶ ⠀⡀⢧⣿⣻⣿⣏⣿⣽⡤⣧⣇⣿⣿⣿⣿⣆⣿⡿⣿⣮⢸⡇⣰⡟⣾⢪⡠⢸⠳ ⠀⠀⠀⡄⡧⣷⣵⣯⣿⣿⣿⡉⣿⣿⣿⣿⡼⡄⣶⣸⣧⢪⣱⡟⣿⣠⠀⠇⠇⠀

⠀⠀⡀⢀⠀⠧⠤⠀⠒⠒⠒⠐⠘⠁⠈⠀⠀⠊⠒⠒⠒⠐⠇⠤⠀⡀⢀⠀⠀ ⠀⠁⠈⠁⠈⠀⢄⠁⠁⠔⠠⠀⢤⠂⢹⠀⠁⠸⢀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢅⠒⠃⢀⠁⠔⡀⢀⡀⡄⠼⣁⣐⣠⣤⢑⠀⠊⠤⡀⣊⣀⠢⠀ ⠁⠀⠀⠀⠋⡜⠑⡄⢄⡠⠒⠁⠉⠀⠀⢸⢱⠀⠀⠀⠁⢿⠉⠀⡜⠀⠀⠀⠰ ⠀⠠⠙⡇⢈⢢⠈⣖⢪⠠⠀⠀⠉⡈⣁⢉⡀⢤⠤⠤⡧⣠⡊⠃⠈⠀⠁⡔⠀ ⠀⠀⡀⠑⢇⠒⢣⡠⠀⠁⠔⣀⠀⠀⡌⠀⢐⠠⠑⠀⡆⠼⢀⡏⣀⠾⢀⠀⠀ ⠀⠀⠀⡀⠡⠹⢩⠊⠄⢀⠀⠀⠁⡼⢸⡀⠀⠀⠀⢄⠈⠀⢀⢱⠞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣣⠢⠁⠈⠀⠀⠋⣿⠀⠆⠘⠀⠀⠀⠀⠀⠢⠉⡌⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⠁⠉⢎⠒⡗⣝⠀⠂⣗⠺⠉⠀⠀⠁⠊⡞⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠛⠗⢘⣄⠜⡠⣦⠵⠮⣾⢀⠀⣄⣑⣥⣛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠓⡋⠺⠉⣏⠟⠛⠚⠁⠣⡡⠒⡠⠀⠀⠀⣦⠘⡲⠒⠁⠀⠀⠀⠀ ⠀⠀⡆⣨⠀⠁⠛⡟⢹⡿⣿⡹⡴⢜⢀⠀⠀⠀⠀⠀⠀⢇⠈⠀⡀⢾⠀⠀⠀ ⠀⠀⠀⠁⢔⢥⡶⣤⣤⣤⣾⢡⡰⠀⠀⠀⠀⠀⠀⠀⠀⡇⢬⠶⣈⠀⠀⠀⠀ ⠀⠀⠎⢃⠔⢀⠀⠀⠁⡰⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⣄⠹⠀⠀⠀ ⠀⠁⢾⢁⠔⠀⠀⠂⢨⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠀⠄⠑⣄⠈⠀⠀ ⠀⡄⢤⠀⠤⠠⢀⠀⡀⠢⠁⠀⠀⠀⠀⠀⠀⠁⠂⡠⠀⡀⡄⠢⠒⢒⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠁⠈⠀⠀⠀⡀⠦⠑⠉⣀⣦⠀⠀⠀⡏⣡⣯⠑⣀⠠⢕⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠺⠀⠐⠀⠀⠀⠀⢄⠸⠀⠀⠀⢀⣰⡀⣀⢄⠌⡘⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⣸⠄⠠⠓⡄⠄⠂⠛⠠⠀⠀⡄⠀⠈⠀⠀⠀⢧⢀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠅⡀⣀⢸⠀⠁⠔⢰⠀⠀⠀⠀⠀⢂⠀⠀⡆⢨⠉⠊⠒⢑⠈⠀ ⠀⠀⠀⠁⠉⡇⠀⠃⠂⡠⢀⠀⠀⠀⠀⠀⡆⠈⠃⡎⢙⠋⣾⣠⠀⡘⠦⡘⠢ ⠀⠀⠀⠀⠁⣔⡠⠄⠐⠀⠀⠁⠀⠀⠀⠗⢥⠠⢣⠖⣷⣽⠉⠈⠁⢩⠈⡂⠻ ⠀⠀⠀⠂⢰⠀⠃⠀⡀⠬⠒⠂⡙⠤⠃⢠⠨⠂⠄⢰⢱⡉⣂⣆⣲⡏⡀⢻⡄ ⠀⠀⠀⠀⠀⠁⠪⡠⢀⠀⡀⢄⠊⣰⣿⠈⢆⠀⡏⠁⠓⢛⠈⠗⠟⢸⠀⡇⠀ ⠡⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⡞⢌⠀⣄⢌⠀⠇⠸⡷⠛⣾⢀⠀⣳⣿⠂⢠⠀ ⠀⢄⠢⣒⠚⠐⠠⢇⢉⠂⡰⡠⠀⠀⠀⠎⠤⠐⢠⠔⣶⠵⠲⠎⣺⢠⢸⠀⠀ ⠀⠀⠀⠃⣰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠇⢠⠀⠀ ⠀⠀⠀⡆⢸⠐⠀⢆⠈⠀⠀⠀⠀⠀⠀⠁⢌⠃⠉⠀⠀⠊⠠⠁⠂⢃⠘⠀⠀ ⠀⠀⠀⠀⢂⠲⠙⠀⠀⠂⠁⠈⠀⠀⠀⡥⠲⠒⡐⣠⣦⡦⣧⠀⠇⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣀⠄⠤⠤⢀⠀⠀⠀⣀⢢⡹⠺⠁⠉⡉⡐⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠋⠀⠀⡆⢸⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⡀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀ ⠈⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢸⠀⠀⢣⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠷⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⣼⣇⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⡀⠸⠀⠃⣠⠀⠀⠀⠀⢄⠲⠉⡎⣻⠘⠀⠀⠈⠀⠀⠉⠊⠒ ⠀⢿⡿⠈⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠀⡇⠉⣸⠀⠀⠀⠀⠀⠀⠀⠁⣏⣈⢤⠤⠤⢤⣠⣍⠀⠀⣀ ⠀⣇⣾⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢻⠀⠀⠁⠋⠖⢤⠤⠤⠤ ⠀⡇⢹⠀⠀⡿⣤⣀⣄⣤⣄⠤⠒⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠲⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠎⣠⠋⠿⣴⣀⠀⠀ ⠀⡇⣿⠟⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠂⠒⠉⠀⠀⠀⡄⣼⠀⡏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⢨⢹⡟⣴⣠⠀⠀⠀⠀ ⠀⡇⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⣼⣄⣦⢵⠛⣈⠳⠀⠀⠀⠀⠀⠀⡀⣆⢸⡆⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠘⠀⣄⣷⠙⢧⠙⠀⠀⠀⠀⠀⠃⢸⠀⣄⠙⠀⠁⠀⠀⠀ ⠀⠀⠀⣆⠻⠙⠈⠀⠆⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⣶⡇⠀⢀⠀⠀⠀⠀⡏⢸⠀⠀⡇⢿⣿⠀⠀⠀ ⠀⠀⠀⠀⣇⢄⢻⠀⠀⡀⣿⠿⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣇⢰⠀⠀⡄⡀⣿⢿⠘⠀ ⠀⠀⠀⠀⠀⢻⣾⠠⠀⠀⡇⣾⠀⠁⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⢿⠀⠀⠀⠀⠁⡸⠀⠀⠀⠀⠀⣿⣿⢿⠀ ⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⣰⢉⠖⣦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠊⣠⠀⠀⠀⠀⠃⡀⣷⣾⣧⠀ ⠀⠄⠤⣀⡁⣾⣑⣊⣶⣻⣉⡛⣾⠹⠁⡚⠶⠒⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⡶⢧⣸⠀⠀⠀⠀⠁⠉⡚⠖⣥⠛⣽⠀ ⠀⠀⠀⠀⡄⢷⡸⢂⠓⣿⣿⣹⠀⡀⣷⠀⠀⠀⠀⣀⢤⠑⠈⠀⠀⠀⠀⠊⣼⠀⠁⠞⣀⠀⠀⣿⣮⣐⣀⣀⣀⢁⠘⠀⠀⡀⣦⣿⠀ ⠀⠀⠀⠀⠀⠀⢄⠤⠄⣶⣽⡞⠘⠀⠀⢄⠛⠀⠀⠀⠀⠆⣶⢿⠸⠒⠓⠒⠚⠤⣄⠢⠑⠁⡿⣿⣀⠀⠀⠀⠀⡋⢿⠺⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⣦⡘⠢⠈⠀⡄⠹⠀⠀⠀⠀⠀⠈⢸⠀⡇⠞⢀⠀⠀⠀⠀⣄⠢⠉⠀⠀⠀⠀⠏⣸⣏⢸⠀⠀⠅⣿⠚ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣄⠙⡇⠉⠉⡏⠳⠈⠀⠀⠀⡇⣴⠤⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⡶⣒⢒⠒⠖⠤⡠⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⣡⣿⣤⣁⢚⠑⢇⠀⠁⠟⢡⠉⠚⢶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⢀⡇⣻⣿⣶⠓⣛⣻⡿⠾⣶⣿⣽⢀⠋⠒⡄⢣⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⠹⡀⣦⣾⣴⠀⠀⠀⠀⠁⠛⡟⣿⣿⠿⠶⠻⢈⣠⣈⢤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⢿⠙⡏⠓⠉⠋⠉⠉⠋⣿⡏⣠⢀⠤⠂⠁⣌⠢⡉⠀⠇⡘⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣯⣵⣻⣿⢻⡿⣾⢀⠀⣷⠚⠉⡉⣈⣤⣦⠱⡈⠱⠀⢶⠘⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡀⠀⡄⣠⠀⢻⠈⠀⡏⢷⠈⠻⡀⣄⠧⠑⠈⠀⢣⠚⡖⠱⠉⢫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢶⡤⣴⢤⠁⠋⠇⣼⢶⡴⢹⡏⢹⡉⢏⠉⡉⢯⡈⠢⠀⢳⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⡙⣍⣋⣞⢺⢠⠀⠀⠀⠀⣀⣄⠦⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠁⡁⢀⠲⠓⠀⠃⠖⠸⢁⠀⠉⠀⠀⠐ ⠀⠀⠀⡅⠐⢀⡀⠑⠐⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⡘⠣⠀⠠⠀⠀⠠⠃⡀⠀⠀⠀⠀⠀ ⠗⠶⡄⣀⡼⠃⠓⡨⠫⠓⠔⡰⠀⠀⠀⠀⠀ ⠀⠀⠂⠴⣿⢠⣀⣤⣠⢀⣇⢼⠲⠀⠀⠀⠀ ⠀⠀⠃⠶⢸⣤⣬⠁⡄⣼⢠⣾⠳⢘⠀⠀⠀ ⠀⠀⠗⠿⣿⣻⣿⢨⣥⣿⣿⢿⠿⢸⠀⠀⠀ ⠀⠀⡄⣷⣿⣿⣿⢻⣿⣿⣿⣿⣴⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣮⣷⣿⣿⣶⣮⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢄⡏⠀⡇⠎⢀⠀⠀⠀⠀⠀⠀

⠀⠝⠈⠡⠀⠀⠁⠀⠀⠀⠈⠂⠒⠐⠈⢡⠀⠀⢇⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⢑⠀⠀⢆⠹⠜⢀⠀⠜⣀⠀⠀⠀⠀⡀⡦⠊⠒⡔⠂⠙⢸⠀⠀⠀⠀⠀⠀ ⠀⢆⠚⡪⢣⢏⠀⡇⠀⠀⠀⠀⠀⠀⠣⠀⣇⠠⢀⠀⡀⣧⠲⠙⠀⠙⠀⠀ ⠀⠀⣡⠱⠀⣤⡤⡶⢕⠠⠀⡠⢀⠔⡟⠒⠐⢼⡏⡼⠠⠸⢆⡩⢿⡟⠹⠀ ⠀⠀⡀⠘⠂⠈⠀⠀⠀⡀⠣⠈⠀⠀⡈⠉⠈⣄⡟⠀⠀⢾⠈⢇⣿⢻⡎⠸ ⠀⠀⠀⠃⠀⡀⠡⠀⠀⠁⡡⢧⠀⠃⢀⣤⢀⠀⢸⠀⠀⣸⡈⡀⣷⣧⢠⢠ ⠀⠀⠀⠀⠳⠉⠉⢇⠍⢔⢀⠀⠁⠨⢀⠥⠑⠀⣄⠀⠄⢼⠐⠈⡆⡜⡎⠈ ⠀⠀⠀⠀⡄⢑⠁⣈⣊⠢⠋⠚⠋⢶⠤⠤⠠⡊⠳⠈⠁⢰⠀⡄⠐⢿⢨⢰ ⠀⠀⠀⠀⠀⠀⣀⢀⠄⠈⡇⠆⢫⠐⠝⠪⠀⡋⠜⣄⣀⣄⠱⠀⡄⢸⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⣿⢼⠥⣰⠆⠤⣤⡤⠶⠀⣀⣧⠀⡇⢂⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣥⢈⣀⠀⠀⢄⠤⢀⠁⠴⣐⣌⠀⡴⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠎⠑⠈⠀⠀⠁⠆⠈⡇⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⠂⠠⣁⣀⣁⣀⢀⢅⠻⠀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠅⢡⠀⠁⢘⠀⠀⣄⠖⢠⠀⠀⠀⠀⠀

⠀⢡⠊⣴⣀⣀⠀⠃⢔⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⡠⠀⠈⠉⠉⠖⣤⢤⠤⠤⠠⠙⠀⠀⠀⠀⠀ ⢤⠙⡈⢀⠀⠀⠀⠀⠀⠂⠒⠁⡈⢿⠴⠁⠚⠀ ⠀⢡⣣⢀⠢⠛⠁⠉⠉⠀⠀⠀⠅⡯⡒⢒⠉⢯ ⠀⡀⠘⢆⠘⣸⡿⣿⣸⠸⠀⠀⠎⢄⠤⠂⡑⢸ ⠀⠀⡆⠘⣇⢠⡦⠓⡄⢺⠟⡩⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⡇⠂⠀⠀⣀⢧⠂⠁⠀⣅⠘⠀⠀⠀ ⠀⠀⠉⡖⢹⠛⠤⠥⢳⡈⠰⡎⠀⠃⢠⠀⠀⠀ ⠀⠆⢸⠀⣄⠈⠆⠠⠀⢻⣞⢀⠁⠰⠀⠀⠀⠀ ⠀⠀⡀⠠⠛⡋⠢⠀⡇⣆⢀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣢⠑⣠⡁⢄⠠⠼⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠠⠤⡔⠈⠇⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣟⣿⣜⡸⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⡿⣼⡯⢮⢵⠂⠈⠀⠀⠀⠀⠀

⠟⣿⣴⣠⢀⠀⠀⠀⠀⠀⠃⠚⠉⠁⠉⠋⠛⠿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇ ⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⣰ ⣀⢻⠶⠶⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠉⠛⠶⣧⣀⠀⠀⣆⠸ ⡇⢠⠀⠀⠤⢀⣸⣄⠦⠲⣛⢮⠀⠈⠀⠀⠓⠉⢞⡴⣦⢉⡴⠁⡼⠀⠀⠀⠁⣼ ⡇⠺⠈⠉⡏⠉⡢⠥⠭⡨⠔⣀⣷⢀⠀⠀⠀⣸⠀⢄⠠⠐⠤⣠⠀⠀⠁⠀⢟⢫ ⢻⢿⡘⠄⢹⠰⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⡠⠋⡿⣿⣿ ⣿⣿⣿⠻⠙⡈⠀⠀⠀⠉⠛⣴⢀⠀⠀⠀⠀⠀⡀⣭⠶⠓⠛⠛⠿⣯⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⣈⣃⣉⢉⠀⠀⠀⠀⠁⠀⠉⢉⠋⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠇⡬⣠⣀⣂⣀⠇⠀⠀⠋⠞⣡⣗⣈⠚⠒⠒⠓⠉⠋⠛⠓⠙⠉⠀⠋⠷⠾⠓⠀⠀⠃⠶⠒⠒⠓⠉⠈ ⠀⠀⠀⠀⠀⣄⠳⠘⠀⠀⡆⠛⡿⣹⠀⡃⠿⣯⠀⠀⠀⠀⡀⢱⠀⠀⠀⡀⢦⣟⡼⣌⡔⠸⠀⣿⠀⠀⠀⠀⠋⣴ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷⣿⣿⢿⡮⣤⢠⠀⠀⠀⠀⠀⡄⠦⠛⠀⠀⠀⡄⡿⣽⠋⡟⡟⢴⠀⠀⠃⣰⠀⠀ ⠀⠂⡾⣀⣅⣇⢀⡇⠘⠀⠀⡄⣾⣠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⡀⣦⣿⣸⢠⠀⠀⡼⠀⠀⠀ ⠇⡞⣤⠲⠉⠈⠖⠒⢻⠀⠀⠀⢇⠀⠀⠀⠁⠊⡤⠀⠀⠀⡀⠐⠂⠀⡄⢦⠙⠀⠀⠀⠀⣞⠀⠀⠀⠇⢠⠀⠀⠀ ⠀⢤⠓⠉⠉⠈⠀⠀⡄⠘⠀⠀⡀⢠⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡀⢆⠑⠈⡆⢀⠀⠀⠁⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⢈⠀⢣⠈⠀⠁⠟⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠉⣄⠳⠈⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢨⠗⠤⣦⣓⢉⠈⣀⣿⢼⠑⠈⠀⠀⠀⠋⡼⢀⠀⠀⠉⡔⣠⠀⠁⠀⣀⢦⣘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⢻⡌⠲⠒⠙⠀⣁⢸⢸⢣⠀⣀⣀⣃⣷⠳⡀⢧⠬⣠⢀⠀⠀⠀⠀⢄⠀⠀⡀⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣿⠷⠛⠉⢍⣋⠞⢸⡇⠀⠀⠀⡇⡄⠀⢧⠉⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡄⣧⠛⢸⡀⠺⣂⠐⠀⠀⢸⡀⣧⣿⣤⠦⠓⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⡆⢸⠀⢀⠀⠀⠀⠀⢃⠉⡉⣋⢿⠟⣿⣿⣨⣀⢯⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠃⠷⠀⠇⠛⡿⣶⣷⣿⣽⣤⣤⣤⣦⣘⣦⣾⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢚⠴⣤⣀⣀⠀⠀⠀⠀⣦⣿⠸⠀⠀⠀⣆⠘⠀⠀⠀⠉⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣾⣠⠉⠋⠰⠀⠀⠁⠉⠋⠛⠓⣟⣿⣾⣶⣶⣶⢻⠀⠀⠀⣤⠀⠀⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣼⠀⠀⣀⢀⠀⠟⡴⣁⣿⣶⣴⡥⢸⣷⣿⠈⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠓⠿⠻⠀⠀⡄⣱⢈⠀⠁⠋⡴⠀⡇⣿⢿⠖⠿⠿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣾⡟⢹⠖⣠⣃⠰⠀⠀⠀⣁⣋⣙⠄⡿⣼⣤⢀⣀⣴⣧⣿⠉⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣻⣿⠺⠛⡴⠁⠋⠟⡼⣷⣿⣿⠻⣿⣠⠀⠀⠁⠉⡏⣿⠀⣄⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠿⠹⣇⣿⣶⢸⡀⣡⣟⣿⣿⢿⠰⠀⠅⡿⣸⣧⠙⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣷⣿⣿⣿⢿⣿⡼⢡⠀⠀⠟⣿⣿⣿⢾⠋⡿⣸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⣻⣿⣿⣿⢻⠟⣿⣿⣿⣿⣼⣠⡀⣷⠻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣤⣷⣹⣀⡇⢸⠀⠀⠀⣆⢿⣿⠙⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⡈⢿⠂⠀⠀⠀⡀⣧⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⡌⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠁⠀⠀⠖⠴⣠⣈⢇⠟⡳⣾⢀⠁⣿⣿⣿⣿⣿⣿⣿⠿⠛⠈⠀⠀⠀⠀⢀⠀⢀⣤⢙⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁⠋⡐⣀⠀⠀⠀⣀⠀⢀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠑⡞⡤⣀⣯⣸⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠉⠀⠀⠀⠀⠀⡁⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢏⣾⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠁⡟⣠⣆⠝⣤⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⢀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠉⠗⡪⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠋⣿⢠⠀⠀⣄⠹⠀⠀⣄⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠉⠀⠀⢦⠙⠀⠀⠀⠀⠆⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀ ⠀⠀⠀⠀⠀⠃⠀⠀⠞⢯⢠⠀⠀⠀⠀⡄⠻⠀⠀⡀⢦⡳⣝⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠉⡄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⠸⠦⢷⠸⠀⠀⠀⠉⡔⢀⠁ ⠀⠀⠀⠀⠀⡇⠁⡜⢇⢰⠀⠀⠀⠈⠀⠀⡄⠹⠀⠀⠀⠀⣀⣤⠦⣛⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠯⠙⠀⠀⠀⠀⠀⠀⠀⡍⣼⢤⠒⡑⢸⠍⠤⣠⢁⠋⠿⢟ ⠀⠀⠀⠀⠀⣿⡼⠃⢸⠀⠀⠀⡤⣏⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠃⣶⣷⡹⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠂⠒⠶⠥⣉⠉⠟⠿⣸⣄⢀⡀⣿⣿⣿⣴⣀⠀ ⠀⠀⠀⠀⠀⣾⠀⡼⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠋⡽⠟⡙⣷⢶⠙⠀⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣀⣀⣀⢀⠀⡀⣿⣿⢸⠁⠋⡷⣿⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⠸⠀⠉⠞⡴⣤⡶⠓⣏⢰⠀⡀⢡⠈⠀⠀⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣠⠀⡞⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠃⢻⠈⠀⠀⠀⠀⠀⠀⠁⠏⣿⣿⣿⢿⡴⣀⠀⠀⠀⠀⠃⣸⠀⠀⠀⡠⢧⠙⠀⠀⠀⠀⡀⣤⣦⣿⣿⣿⣰⠀⠆⡿⠹⠟⠾⠀⠀⡆⣿⣷⠸⠁⢸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⣄⠦⠙⠀⠀⠀⠃⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠋⡿⣴⠀⠀⠀⠀⠀⡀⡀⣄⠿⠼⠶⠴⠤⣧⣈⣀⣠⠀⠀⠀⣇⡛⣛⢛⠀⠋⡾⣏⡆⢸⡇⢠⢀⠀⠂⠙⠀⠀ ⠀⠀⠀⠀⡆⢀⠀⠀⠃⣿⣿⠿⠟⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⡗⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⣄⠶⠙⠉⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⣽⠆⣿⠀⢦⡄⠀⠀⠀⠀⡀⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠁⠀⠀⠀⠀⠀⠀⣦⠈⠀⠀⠀⣀⢦⠳⣯⠻⠈⠀⠀⠀⠀⠀⠀⢸⣄⣧⠾⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⠌⢠⠀⠀⠀⠀⠁⠋⠟⢻⠈⠀⠀⠀⠀⠀⡀⣄⣷⠹⠀⠀⠀⠀⠀⢠⡿⣄⢲⠙⠈⠀⣄⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠏⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠙⠈⠉⠟⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠘⠀⠀⠀⡟⣿⣧⠫⠛⣿⠘⠀⣆⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠆⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠁⡿⣿⣿⡇⣛⠀⠀⣾⠀⠀⣿⠛⠛⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣾⡇⣿⠀⡆⢶⡴⣠⣏⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⡄⢸⢸⠀⠀⠃⣾⢒⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⠘⢀⢳⠀⠄⠷⠿⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⠳⡝⠨⠀⡄⣧⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠞⡠⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣾⠙⣀⠦⠙⡆⢸⠀⠀⠀⠏ ⠀⣿⢰⠀⠀⠀⠃⡾⢀⠀⠇⢰⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣾⠹⠀⡀⢦⢸⠀⠀⠀⢲ ⠀⢰⠀⠀⠀⠇⣼⢀⠀⠀⡼⠀⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⡿⠘⠀⣆⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠀⠀⠀⠃⢰⠏⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⡹⣄⠲⠙⠀⣿⠸⠀⠀⠀⠏⠴⣽⣫⣍⠿⠙⠀⠀⠀⣇⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⡇⠏⣯⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⡝⠸⠀⡀⢄⣗⣆⠘⡄⢷⣿⣭⣋⣟⣿⣿⣿⢻⠛⠟⡿⣿⣿⣿⣿⣧⣈⠀⠀⠀⠀ ⠀⠀⠀⠟⢀⠀⠀⠀⠀⡟⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠹⠀⠀⠀⠀⣄⠹⠀⡀⣦⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⢙⣧⣿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⡿⢰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡶⣠⣋⠟⠻⠈⠀⠉⠀⠀⠓⠈⠀⡀⣧⢮⠙⠀⠀⠀⡀⢢⠈⠀⠀⣀⣀⢀⣄⠳⠈⣀⣀⠀⠀⡜⡇⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢇⢸⠀⢸⠀⠀⠀⠁⠹⠀⠀⠁⠏⣾⢶⠶⣷⣿⣿⣿⢿⣼⢀⠀⠀⡀⣧⠦⠘⠇⢧⡜⠹⠀⠀⠀⠀⡀⠢⠉⠀⠀⡀⣄⣶⣷⠹⠀⠀⠁⢰⡌⢸⡆⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢀⡾⠀⡇⢈⠀⠀⠋⣿⣿⣿⡿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣶⠠⠉⠚⠤⠀⡀⢸⣄⣷⡈⢧⡀⠘⠀⠀⠀⠀⠀⣄⢷⠛⠉⠀⠀⠀⣣⢯⠈⡆⠀⢷⢸⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠙⡏⣿⠿⡿⣦⣙⣀⣒⣟⣿⣽⣭⣭⣿⣾⣤⣤⠤⡤⣠⣀⠁⠚⠀⠀⣧⠀⡀⢳⡀⢻⢣⠈⠀⠀⠀⠀⠀⠀⣦⡹⣦⣻⣀⣄⣹⣦⣜⠤⡧⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⣈⣦⢿⣙⢷⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⡴⣠⠀⠀⠀⡆⠸⠀⡀⢳⡀⣱⢳⠀⠀⠀⠀⠀⠀⠀⣆⠻⠈⣄⠙⡏⠈⢧⠈⡏⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⡀⣳⢳⣮⢮⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢿⠪⠐⡆⠘⡆⡈⢹⠀⠀⠀⠀⠀⠀⠀⡄⢿⠀⡀⣦⢸⠀⢷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⣄⣿⡘⢷⢸⠀⠀⠀⠀⠀⠀⠀⠉⠋⠒⡴⣠⣀⣄⠀⠀⠀⠀⢷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠀⠀⣧⠘⡀⣿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⡀⣀⢉⡃⠁⠃⢠⢠⡇⢴⠀⠏⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⠛⠚⠶⡶⠶⠒⠙⠈⠂⠈⠀⣻⣓⠀⣇⠙⠟⣠⠀⡌⣿⠀⠀ ⠂⠚⠮⡷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠱⣀⣀⠃⣿⡻⣿⠀⠁⣵⣸⠆⠀ ⠄⠏⢀⡟⣿⢰⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢣⠰⢀⡳⢃⢀⠀⡀⠛⡠⣀⠐⠘⠀ ⠈⣧⠱⣇⣼⠀⡡⣀⢀⡄⠫⠈⠀⠀⠀⠀⠀⢢⠈⡀⢐⢦⣬⣷⢻⠸⠛⢀⠀⠀ ⠀⠈⢂⣈⢠⠀⠀⢿⣿⣿⣿⢰⠀⠀⠀⠄⠦⠲⣝⠪⡈⠢⡈⠢⡈⢤⡗⢻⠀⠀ ⠀⠄⠑⡄⠘⠀⠀⣽⣢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡂⠈⡀⠢⣂⠌⠈⢠⡘⠁ ⠠⠑⠈⣀⢣⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⠐⠄⡧⠺⠀⡀⠀⡀⠀⠆⡤ ⠀⠀⣦⣿⡙⠳⠒⠉⠋⠀⠀⠹⠀⠈⠀⠆⡹⢀⠉⠟⠞⣧⢣⢃⠈⡀⠢⠀⠀⠀ ⠀⠀⠀⡀⣏⠘⢷⡻⠻⢿⠈⠘⠰⢜⠈⠀⣀⣴⣠⣀⠋⠘⡏⠀⠆⠈⠀⠀⠀⠀ ⠀⠀⠀⠆⡷⢣⡀⣧⠐⠄⡇⣿⡄⢸⢆⠘⠀⡀⠠⣁⣾⣠⠀⠀⠀⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⡹⡘⠑⠀⡄⠢⡞⣇⠰⡄⠀⣡⠢⠉⠔⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⡀⢦⠘⠢⠈⠀⡀⢸⡱⠀⢠⠀⠡⡀⠠⠑⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⡑⠠⠐⠌⠀⠣⠈⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠤⠒⢊⠈⣄⠰⠈⠀⠀⠀⠀⠀⠀⠁⠊⡲⠠⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠚⠚⠑⠀⡇⠑⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⣠⢢⠈⢄⢸⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡼⠡⡀⠱⠉⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀ ⠄⠢⠁⠀⠂⠀⠀⠀⠀⠄⠠⠰⠀⠀⠦⡷⣒⢖⠈⢢⢫⠈⡀⠥⠃⠈⠀⠀⠀⠀ ⠀⠀⠀⡀⢠⠑⡇⠉⠉⠛⠛⡞⠐⠀⠀⠀⡀⣄⢶⠙⢆⢹⣁⠹⢄⣷⠘⠀⠀⠀ ⢀⠩⠐⠉⠀⠀⣀⣦⣿⢰⢀⠡⠀⡀⠄⠠⠑⠀⠌⢑⣡⡌⢻⡨⠘⡏⣀⠙⠀⠀ ⡃⢒⠷⠶⣼⠓⠀⠀⡄⠀⠄⠟⣶⣴⠻⠘⠀⠢⣫⠱⡣⢹⡄⠘⠇⣶⠀⣿⠺⠈ ⢶⡤⠐⣼⠙⡏⠠⠀⠀⠀⠀⣹⠀⠏⣿⣿⠀⠀⠀⠀⣃⣾⠱⡀⡐⠱⠁⣸⠛⣌ ⡄⣬⣶⣦⡯⣿⢸⠀⠀⠃⠀⡅⣦⣶⣴⣠⠀⠀⠋⡿⣶⠱⡚⠹⡀⠐⡱⠟⣏⢰ ⢄⠦⠡⡄⢹⡀⣤⠀⠘⠱⢕⡸⠀⠂⠠⠀⠠⠢⣟⣵⠹⡐⣀⡑⠱⡆⡆⢴⢀⠀ ⠀⠀⣇⡏⣤⠹⠋⠆⡛⠫⣫⢱⠉⠛⠿⠱⠇⢆⢁⡀⢱⠃⠿⠿⣿⠘⢹⠳⠈⠀ ⠀⠀⡇⠀⢄⡾⣷⢭⡦⣿⣄⣄⣹⢙⠈⡆⣾⠹⠀⠢⡀⡐⣧⣿⣟⢮⡏⠀⢄⠑ ⠀⠀⡇⠀⡎⢘⠀⡀⢤⡛⢮⢾⡈⢤⠉⠀⣟⣬⢢⠈⢀⡀⣣⣧⡘⣁⡿⠙⠀⡄ ⠀⠀⡏⠆⡀⠀⠀⠀⠀⠀⣄⠵⡦⠲⡉⡦⣿⣿⠿⡙⠉⠉⠒⣟⢟⣴⠀⠀⠀⡀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠵⣈⡤⢳⣧⣶⢠⠋⡾⢤⢀⠀⠀⠀⠀⠀ ⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⢀⡤⣦⠤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠇⠀⠀⡇⠀⠀⠉⠀⠁⢠⠙⠀⡇⠀⠈⠒⠒⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠈⡆⠠⢀⠀⠀⡉⠔⣀⠁⡀⡞⠀⠀⡐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⡠⠀⠀⢄⠀⠀⡞⣠⠛⠹⡀⢄⣷⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀ ⠀⢰⠀⠁⠉⠛⠟⡿⢿⣿⣿⣶⢿⠉⡁⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀ ⠀⠿⡿⣿⣿⣴⣠⣀⠀⠀⠀⠀⡄⣿⠸⣆⣹⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠇⣿⣿⣴⠀⠀⠉⠉⠉⠋⡜⣯⣿⣿⢀⠀⡇⢼⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣴⢀⠀⠀⡀⠀⠀⠗⡿⡶⣷⣾⢀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠋⠀⠊⠶⣠⠒⠀⡀⢰⠁⠁⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⢩⡴⠒⠀⠈⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠀⠄⠀⠀⠀⠄⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⡉⢋⣿⠀⡇⢙⠀⠀⠀⠀⠀⢀⣀⠀⣄⣶⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀ ⠄⠀⠄⠁⠄⠁⡏⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡾⣿⣛⡿⣶⣤⣧⠘⠉⣌⠳⠉⠋⠛⠙⠉⠛⠛⠉⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠙⠄⠁⠄⡁⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠟⠶⡤⣤⣉⢟⡴⣠⢀⠀⠀⠀⡟⣸⠀⠀⡠⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⢯⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠿⠉⠆⣿⣿⣿⢠⠀⠀⠁⠉⠉⠛⠟⠿⡿⣿⣿⣿⢿⠿⠿⣿⣴⣠⢀⠀⠀⠀⠀⠀⡏⣴⠀⠀⠀⠀⠀⣳⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⣆⣻⠏⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠁⠞⣤⢀⠀⠀⠉⠀⠀⠀⡄⠹⠀⡀⣄⣶⣿⣿⣿⡿⣴⠀⠏⣿⣿⣿⣿⢿⠻⠙⠈⠀⠀⠀⠀ ⣦⣿⠻⣌⣷⣿⡾⠀⣿⣿⣿⣿⣿⣽⣀⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠟⣶⠳⣼⠀⠀⠀⠀⠀⣯⢠⠀⠀⠀⣷⠀⠀⠀⠀⡀⣤⣷⣿⠀⠀⣿⣽⣄⣶⣶⣶⣷⣶⣿⢿⠛⠙⠈ ⠀⡀⣦⢱⡾⣿⢣⠈⣶⣷⣹⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡄⠻⡼⠉⠎⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣄⢦⠓⡏⣻⣿⡿⣿⣿⣿⣿⡾⣠⠀⡁⣿ ⠀⠀⠀⡀⣿⣤⠀⣿⠈⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⢈⢀⠀⠀⠀⡇⣾⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣟⣿⣶⣶⣿⣿⣿⣠⠀⠀⠁⣿⣥ ⢳⠀⠀⠀⣇⠀⠀⡇⣿⡿⣿⣿⣿⣾⣠⠀⠀⠆⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⠀⠀⠀⠀⠁⡿⢻⠀⠀⠀⡇⣿⠹⠀⠀⠀⠀⠀⡄⣣⢛⠙⠀⣀⣆⠻⡙⣀⢦⠓⠈⠀⡇⣿⣠ ⡀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡿⢿⠈⠀⠀⠉⠟⣿⣿⣿⠻⠈⠋⡿⣿⣿⠹⠀⠀⠀⠀⠀⡄⠾⣄⠀⠀⠀⣄⣿⣿⠻⠀⣀⣤⡿⣿⠀ ⠀⠄⠀⠀⡆⠀⠀⠀⣿⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⣿⡻⢷⠈⠀⡀⣷⠈ ⠀⠀⠇⠀⡀⠀⠀⠀⣧⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⣾⣠⣄⣶⠀⠀⠀⠀⠀⡄⣤⢤⠿⠙⠈⣇⣿⣻⢿⠀⠀⡀⣿ ⠀⠁⠐⠁⠀⠀⠀⠀⡇⠀⢿⠰⠀⠀⠀⠉⠋⠛⠖⠰⠀⠀⠀⠀⠀⡿⣿⣶⣶⣷⢉⣌⣦⣶⣶⣤⣤⣠⣁⠋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⡞⢠⡌⣶⠿⣟⣿⣿⢹⠀⠀⡇ ⢿⡸⠀⡀⠸⠀⠀⠀⡇⠡⣸⠁⠋⠵⣿⣴⣀⠀⠀⠀⠀⠀⠀⠁⡾⣠⠀⠀⠀⠀⠀⣀⣤⢤⠲⠴⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⢈⠃⡼⠃⡽⠀⠆⣧⣿⣷⣿⣿⠀⠀⡄ ⣿⢸⠀⠀⢀⠀⠀⠀⡇⡿⢾⣠⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣫⡴⠟⣰⠋⣿⣵⡼⠀⡄⣿⡹⢰⣿⠀⠀⠀ ⡜⢻⠀⠀⠀⠀⠀⠀⡏⣰⠀⠏⣠⠀⠀⠟⠷⠐⠀⠀⠁⠞⣠⠤⠁⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡴⢞⣡⡾⢥⡿⣤⢣⡾⢤⠩⠀⡇⣿⠸⣧⠘⠀⠀ ⣆⣇⠸⠀⡃⠀⠀⠀⡇⠀⡇⣰⠀⠀⠀⢰⡿⠡⠊⠛⣱⠘⠀⠞⣠⠀⠐⠁⠚⠀⠈⡋⠑⠜⢀⠀⠀⠀⠀⠂⠈⠀⠀⡤⢏⣠⡔⢞⣠⠃⡽⣉⠟⣿⢩⡯⢛⠀⡀⡆⢻⡀⢸⠀⠀ ⠀⣧⢿⠀⡇⠀⠀⠀⡄⠀⣼⢿⠈⠀⠋⡱⢞⣣⡼⢋⡰⠋⡴⢉⠀⠃⠞⣠⠋⡿⡵⢞⣠⠀⠀⠀⠀⠀⠀⠀⣆⠙⠋⡴⢀⠄⡤⢤⠤⣤⣤⣠⣀⠀⡀⣥⣿⢻⠘⠀⣿⠘⢰⠀⠀ ⠀⠀⡇⢻⡏⠀⠀⠀⠀⡇⢠⡇⢿⠏⣾⣡⠞⣯⣴⢋⡴⢂⡠⢃⠟⣠⢟⡶⣷⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢘⠀⠀⠀⠋⠶⠴⠷⠙⠀⠀⠀⠀⡅⣿⣿⣿⡿⣿⢰⠀⠀⠀ ⠀⠀⠀⣇⣿⢸⠀⠀⠀⡟⠀⡇⣟⣴⢸⡳⡘⢋⡵⢋⠟⠛⠟⠻⠖⣷⡿⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣟⠿⠿⠻⡛⢿⠉⠉⠟⣿⣿⣷⣿⣿⣿⠈⠀⠀⠉ ⠀⠀⠀⠀⣷⣿⠀⠀⠀⣻⠀⡀⣿⠀⢸⠀⣁⠞⣠⢄⠤⠤⠤⣤⣀⣀⠁⠘⠈⠀⠀⠟⠸⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⡄⢷⣿⣯⣶⣶⣶⣷⣿⣿⣾⣴⢀⠀⢿⣧⣶⠶⠶⡴⣄ ⠀⠀⠀⠀⡆⣿⠘⠀⠀⣤⠀⠀⢸⠀⢸⠁⡿⢠⠀⠀⠀⠀⠀⠀⠃⡴⣀⣀⣄⢷⡿⣾⢩⠀⠀⠀⠀⠀⠀⠀⡇⢻⠈⠀⠀⠀⣧⣴⣤⣤⣤⣤⣈⠀⠀⠀⠀⡀⣿⡆⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢹⠀⠀⠀⠀⡇⢀⠀⣿⡟⣿⠹⠀⠀⠀⠀⠀⠀⣼⠁⠟⡿⣿⣿⣴⢏⣹⠉⠀⠀⠀⠀⠋⠙⡀⣆⢿⠀⠀⠀⡀⢿⠉⠉⠉⠋⣷⠻⠉⠀⠁⠛⡿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠘⠀⠀⠀⡄⠀⠀⣿⠀⣴⣶⣿⠿⠻⠛⠛⠛⣿⣿⣿⣶⣤⢋⡿⣴⣠⣆⣤⣤⠤⣤⢡⡌⢷⠛⣯⠘⠀⠀⠀⡇⡘⣀⣀⠀⡀⣸⣷⢷⣴⣠⡇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠃⠈⠀⡇⢸⠀⠀⠀⣀⣀⣄⣭⣬⣈⣁⠛⠿⡿⣲⢶⠠⠛⠉⠉⠉⠋⠞⣴⢿⡀⣿⢮⣿⠂⠗⠿⡿⢸⠀⠀⠀⠀⢧⡀⣽⢷⠻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⡇⢻⠇⠈⣷⠈⠀⠀⠀⠀⠁⡼⣻⣽⣀⣰⣀⠀⠀⠀⠁⡏⣿⣿⣀⣀⠀⠀⡆⣿⣿⢀⣦⠹⠀⠀⡀⢻⠀⠀⠀⠀⡇⠸⡇⡸⣿⣼⠀⠀⠀⠀⠀⠀ ⠴⢠⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⣿⡜⢿⡝⢹⠇⠷⠀⠀⡿⢀⣷⡘⣿⠳⠛⠛⠟⡿⣿⣾⣷⣄⠀⠀⠀⠀⠀⣿⣼⢸⠀⣇⠸⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⢷⣟⢰⠀⠀⠀⠀⠀⠀ ⠀⡀⠸⠀⠀⠀⠀⠀⣇⠸⠀⠀⡆⣾⣿⡀⣄⣠⡄⣿⠶⣼⠀⡄⣿⣿⠀⠀⠀⠀⠀⡄⢻⡇⢹⠀⠀⠀⠀⠀⣇⢸⢻⠀⠀⣧⠹⠀⣼⠀⠀⠀⠀⡇⢠⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠙⠀⠀⠀⠀⠀⣧⠈⠀⠀⢧⣎⢹⠀⠀⠀⣧⠸⢸⠀⠀⢿⣷⢹⠀⠀⠀⠀⠀⣧⡟⣿⠀⠀⠀⠀⠀⡄⢹⡇⠀⠀⡄⣿⢿⢠⠀⠀⠀⠀⡇⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢷⠈⠀⡀⢿⣆⠹⠀⠀⠀⣇⢻⠀⠀⣼⢻⣧⠸⠀⠀⠀⠀⡀⣿⡆⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⢳⠈⠀⡀⢳⠀⠀⠀⠀⠀⣦⠐⠀⣇⡄⢹⣄⠀⠀⠀⠀⠀⣆⠘⢸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⣿⠀⠀⠀⠀⠃⢰⠀⠉⡟⠉⠉⠋⠂⠒⠒⠄⠤ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⢷⠘⠀⡄⢻⠉⠀⠀⠀⠀⠀⠀⡄⢱⣆⠹⠈⠀⠀⠀⠀⠀⣀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢹⠉⠛⠛⠶⠶⠤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡀⣄⢦⠛⢈⣏⠻⡟⠭⢻⠉⠙⣉⠤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠁⠋⠖⣩⢛⠟⠴⣤⣀⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀ ⠠⠀⠀⠀⠀⠀⠃⠛⠙⡏⣶⣶⠙⡝⢤⣤⣤⠤⡦⣶⣶⠶⠶⡶⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠾⠴⠤⢧⣿⣾⣶⣴⣤⣠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀ ⣄⢿⠿⡿⣿⣽⢀⣧⣿⣽⠮⠛⣿⣼⠲⠙⠈⠀⠀⠀⠀⠀⠀⠁⠚⡀⣄⢦⡛⣉⣤⣦⣶⣿⣭⢉⠟⡽⣩⣈⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⡄⢀⣀⣤⣼⢆⣻⣿⣿⣿⣸⣤⣦⣷⣾⡶⣿⠿⠙⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⣉⣙⣭⠿⠿⡲⣙⡿⣻⠛⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠉⠀ ⠀⠄⠻⠀⢸⠀⣷⢧⡿⣿⣽⠳⠈⡀⢦⠘⠀⣦⣿⢻⠀⠃⣰⠀⠀⠀⠁⠍⣫⠛⠉⠉⠀⡀⣄⡶⣶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣱⠋⡴⢀⠉ ⠀⠀⣇⢿⢛⠀⠃⡀⣿⣿⣿⡻⣿⠹⠀⣿⢸⠀⡆⣿⠀⣀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⡤⣀⠀⠀⠀⠁⠾⣠ ⠀⠀⡇⡀⣦⢹⠀⠀⡂⣷⣿⣿⣿⣿⠿⣿⣿⠉⠀⣿⠀⠸⠀⠀⠋⣿⣿⣿⣤⣠⣀⠀⠀⠀⣀⣀⣀⢤⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⡿⣩⣀⢉⣭⢀⠀⠀⠀⠁⠋⠖⣠⠀⠀ ⠀⠀⠀⠀⠏⣿⢳⠙⠀⠀⣄⣿⣿⣿⣿⣿⣿⣽⢀⣿⠀⢧⠁⠏⣿⣿⣿⣤⡤⣋⣀⣀⣀⢄⠤⠤⠤⠲⠓⠛⠛⠛⠘⠀⠀⠀⠀⠀⠃⡟⣿⣘⢧⠙⣀⣀⢤⠧⣬⣾⠹⠀⠀⠀⠀ ⠀⠀⠀⠆⣿⣿⠰⣆⠉⡀⠹⡀⣿⣿⣿⣿⣿⣿⠀⣿⠀⡿⡟⣿⣾⣠⢀⠀⠀⡠⢄⠵⠿⠴⣤⣀⣋⣾⣶⢀⠀⠀⠋⣗⣿⣿⣸⣆⣿⡟⣿⢿⠀⣧⢻⠀⠀⠀⢆⣇⣇⠘⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⢹⠛⠛⠛⡟⢿⡞⣷⣼⣾⣿⣰⠀⣤⡦⣿⣾⣠⠀⠀⠀⠀⠁⢡⢟⣰⢀⠀⠐⡤⣉⠚⠒⠴⡤⣤⢀⠘⡀⣷⣿⡿⣿⣿⣿⣿⠀⠳⣽⠸⠀⠀⠀⣿⡟⢿⠀⠀⠀ ⠀⠀⠀⠀⡀⣧⣿⣿⣼⣷⣿⣿⢻⡿⢋⣿⢹⠉⠉⠉⠉⣼⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠋⠔⣡⣿⣿⠈⠀⠀⠀⠀⠤⠲⠙⣏⣿⣿⣿⣿⣿⠘⡇⡏⣿⠀⠀⠁⣿⢸⣾⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⣿⣿⣿⡏⣽⣿⣿⣾⣿⣶⣿⣿⣾⣣⣷⢸⠀⠀⠀⠀⠉⠈⡇⣿⠃⠶⣠⠀⠁⡿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⣦⣿⣯⣿⣿⣿⢹⣿⣸⣿⢸⠁⡿⣴⡇⢰⠀⠀⠉ ⢿⠈⠀⠀⠀⠀⡄⣼⣿⣿⣿⣿⣿⢸⢹⠀⡏⣿⢠⡿⣼⠀⠀⠃⠕⡨⣀⠀⡆⣿⠛⠉⠛⠿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⣤⣠⣧⣿⣤⣦⣿⣿⢿⡟⣼⠀⡴⠋⠚⡤⣤ ⣿⢿⠘⠀⠀⠀⠀⢿⣟⣿⣿⣿⢼⢘⣿⣤⣦⢠⡞⣿⢠⠁⠋⡾⣠⣀⠀⠀⠃⣶⣷⣿⣿⣿⣶⣴⣤⣩⣎⢲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⣿⢹⠈⣧⣿⣿⣷⠐⠃⡾⣀⠀⠀⠀ ⣿⡀⣧⠹⠀⠀⠀⣦⣿⣿⣿⣿⢈⣿⢩⠘⠀⡏⣯⣾⠟⣷⣿⢀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣄⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠙⣇⣿⣿⣺⣆⣿⣿⣿⣿⣿⠛⣰⠀⠀⠀⠀⠀ ⣿⠈⡄⣿⠹⡄⠈⠀⠃⡆⣿⣿⢸⣠⣆⣸⠃⣷⣿⢿⢰⡟⣰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡉⣿⣿⣿⢿⠿⣿⡿⣿⣿⡿⣿⢿⠘⠀⠀⠀⠀ ⣿⢸⠀⡆⣿⠹⠀⠀⠀⠀⣆⣿⢸⠇⠀⢿⡿⣼⡇⣿⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠛⠟⠿⣶⣶⣶⣤⣤⣧⣿⢀⠀⡖⣷⣿⣿⣿⣿⣿⢹⣿⡄⣿⠘⠀⠀⠀ ⣿⣿⠀⠀⣧⣿⠘⠂⠀⠀⠀⣧⣿⡌⠀⣧⣿⠀⡇⣿⢹⠋⠛⠛⠛⠟⠿⠿⠿⡿⣿⣿⣿⣶⣤⣷⣿⣠⣀⣀⠉⠋⠀⠀⠀⠀⡤⣤⠀⠀⠉⡏⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⠀⠀⠀ ⡈⣷⢹⠀⠀⣷⣿⠫⠀⠀⠀⠀⣷⢹⠀⣿⣾⠀⡀⣿⣿⣿⣿⣶⣷⣿⣾⣠⣀⣐⠀⡇⣿⠀⠀⠀⣦⠐⠀⡇⣴⣀⠀⠁⠈⠀⠃⠿⠘⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⣿⠸⠸⠀ ⢉⠛⣞⢿⠙⡄⣿⢻⠀⢠⠀⠀⡄⣻⠀⣧⠸⠀⠃⣿⣾⢀⠀⠀⡀⣀⢀⠀⠏⠸⠀⡇⣿⠀⠀⠙⠀⠀⠀⠇⡾⢰⠀⡀⢠⠀⡇⣿⢻⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢹⢸⠀ ⣷⣘⠅⠀⢀⠘⡀⣿⢱⠀⠀⠀⠀⣇⠸⡇⣿⡿⣤⣤⢠⠀⠀⠀⠁⡿⢚⠃⡿⢰⠀⡆⣴⠀⠀⣿⠻⠈⠉⠉⠋⠛⠿⠿⣿⣿⣿⣽⣩⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⡇⣿⠈⠀ ⠀⠀⠤⠤⢁⠨⠂⡀⡰⠐⠃⠀⠀⡀⣿⡏⣶⣷⢳⠛⡟⠀⠀⠛⡬⢠⠀⣿⢁⠉⠉⠋⠛⠛⠿⣿⣿⣿⣷⣿⣴⣯⣿⢹⠁⣿⣿⣿⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠿⡿⣼⢸⠀ ⠶⠶⠶⠶⠷⣿⠻⣹⠈⠀⠀⠡⠱⠈⡆⣹⡀⠀⣿⣿⣿⠉⠋⡟⢿⠿⡿⣿⣿⣿⣾⣶⣿⣴⣠⣣⢘⠀⡇⣿⠀⣷⣿⣿⡽⣍⣟⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣤⣷⢛⠉⠓ ⣤⠲⠙⠉⠀⡀⣿⣿⣽⣤⠿⠿⡀⢷⠐⣧⠘⠇⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⢙⠉⠉⠛⣿⢼⠦⣿⢿⠷⡆⣿⣤⠩⣿⣿⣿⣶⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣷⣾⣤⣦⣶⢲ ⠀⢹⡀⣄⢷⠙⢀⣼⣮⢿⡘⣷⣿⣻⢿⡿⣿⡝⣷⣴⣧⣿⢿⠘⠈⣇⣿⣿⣟⠘⡄⠸⣿⢿⠀⣿⣿⡿⠀⣿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣟⣿⣼⠀⠀⠀⠀⠀ ⠀⡄⠘⠀⡠⣷⢿⠛⡈⡀⢷⠉⣧⣿⣿⣿⣿⣿⡈⢆⡌⣷⣿⣿⣿⡻⣿⣿⣿⣿⠉⢹⣿⣿⢸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡟⣿⣠⠁⠈⠀⠀⠀⠀ ⠀⠀⡄⠳⡀⡠⣷⣿⢿⠿⠉⡈⠁⣏⣿⣿⣿⣿⢿⠀⠟⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣳⠛⡿⣴⢫⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠳⡀⣧⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣡⣉⠛⠿⡿⣱⣟⣴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠳⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⠿⣿⣿⣿⣾⣿⣲⡙⢎⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⢿⡟⣿⣾⣤⡟⣏⣿⠟⣿⣿⣿⣿⣿⣿⣿⣻⣴⣠⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣟⣻⣉⣍⣿⢻⣉⣿⠻⣿⠿⠻⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠖⣶⠶⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣻⠀⠀⣄⠷⠝⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣡⠋⠞⣴⣤⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣆⣽⠀⠀⣀⣯⢻⠾⣶⣴⣤⢀⠀⠀⠀⣀⣁⠞⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠙⠟⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠇⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠞⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⢿⠻⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣶⣠⣀⣀⣄⣠⣀⣀⣀⣀⣄⣤⠾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⠀⠀⠀⠀⡿⣶⠤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠉⠉⠀⠀⠀⣇⣿⣿⣚⣴⠤⠦⠛⠙⠀⠀⠀ ⠀⠀⠃⣹⣄⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢶⠉⠀⣿⣸⠀⠋⠗⠾⣦⣲⢙⠀⠀ ⠀⠀⡄⣾⠀⣧⢀⡀⣄⢦⠳⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⣷⢹⠉⡋⠙⠈⠀⠀⢦⢗⠙ ⠀⠀⠀⣆⠘⡀⢷⠈⠀⠀⡀⣧⣿⣤⣥⠿⠻⠒⠚⠛⠚⠓⠘⠀⠀⠀⠀⠄⠤⡾⣤⣠⣀⡀⣤⢦⠷⠚⠚⣶ ⠀⠀⠀⠀⣷⠘⠀⣦⠹⠀⠀⡇⣼⢇⣿⣿⣿⡿⢻⡄⠸⠀⠀⠀⠀⠀⠀⠃⡿⢋⠒⠷⡽⢉⠀⠀⡀⣧⢸⠀ ⠀⠀⠀⠀⡀⢻⠈⠀⡀⢻⠈⡇⢀⡄⣿⣿⣶⣶⢻⠃⣼⠀⠀⠀⠀⠁⠟⣤⣀⠀⠀⠀⠀⣀⣄⠦⠳⡙⢸⠀ ⠀⠀⠀⠀⠀⡆⠻⠀⠀⡆⣿⣿⠘⠿⣿⣿⠀⠀⡄⣿⢸⠀⠀⠁⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀ ⠀⠀⠀⠀⠀⠀⣧⠾⠀⠀⣇⣸⠀⡁⣄⣶⠿⡤⠀⡆⣾⠾⠿⣿⢻⠛⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⡟⢸⠀⡟⠀⠀⡀⣥⠶⠓⣟⢨⠘⠀⡀⣀⢀⡄⣄⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⣿⠀⠇⢠⠀⠀⠀⣿⠀⠀⣄⣸⢤⠲⠙⠉⠀⠀⠀⠀⣅⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢠⠀⡀⠀⠀⠀⠀⣄⠸⠀⠀⣇⠈⠀⠀⣇⢼⠤⠤⠤⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⣟⢹⠀⠁⠞⠴⣠⣀⣄⠦⣷⠻⠈⡀⢷⠈⠀⣾⢠⠀⠀⠁⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡿⢤⢠⠀⣗⠿⣾⣴⣀⣁⣈⣄⠤⡐⣧⣿⠠⡁⢹⡟⢀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣿⢹⠀⠀⠀⠀⣇⢈⠀⠀⡿⢽⠀⠀⠀⠀⣿⢻⡅⣿⣰⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣷⠈⠀⠀⠀⠀⢦⠈⠀⡀⢀⠀⠀⠀⠃⣿⣿⡟⣰⠀⠀⠀⠐⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠲⠙⠈⠀⠀⡄⠲⠉⠀⠀⠀⠇⣽⣧⣿⢠⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠿⡝⠩⡈⠠⠀⠀⣇⣽⡀⣠⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⡹⣦⢻⢀⡡⣄⠢⠒⣆⠶⠙⠉⠉⠉⠛⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠓⡿⠀⠀⠂⠈⠀⠀⣀⣀⣏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡄⠿⠼⠤⠧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⣸⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⣇⢪⠈⠀⣇⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣸⢀⡴⣄⠲⡽⢌⠀⠀⡆⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠻⠙⠉⠉⠉⡋⣛⣿⠻⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣡⣀⣿⣿⢻⡈⣧⡿⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣶⣷⢿⢹⢸⡇⢸⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢿⡿⣿⣽⣸⠑⣯⣿⠿⣻⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⢜⠩⡿⣿⠘⣄⣤⢳⡈⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣸⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣩⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⣄⠦⠛⠙⠉⠉⠀⠉⠋⠟⣿⣷⠿⠙⠉⠈⠁⠉⠉⠋⠞⡤⣇⣿⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠃⣰⠀⠀⠀⠀⣿⣰⢀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⢷⠶⣿⣻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⠀⠀⠀⡤⠀⠀⠀⠀⠁⣾⢴⣤⣤⠤⠤⣤⣦⢹⠀⠀⠀⠀⡀⠀⣄⣰⠀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣬⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠀⠀⠀⠀⠁⠟⣥⢻⠛⠿⠠⠀⠇⠿⡿⣛⣖⢳⠈⠁⠉⠉⠟⣲⣒⣟⠿⠿⠀⠀⠃⠛⠙⡿⢨⠀⠀⡀⢤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠟⠿⣿⣿⣿⣿⣿⣾⠴⣠⣀⠀⠀⠀⠀⠀⣄⣶⣿⣶⣠⠀⠀⠀⠀⡀⣀⢤⡦⣿⣿⣿⣿⣿⠿⠛⠙⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠏⣿⣿⣶⣤⣤⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣤⣦⣶⣿⢿⠀⡀⢦⠙⠀⠀⠀⠀⠀ ⠀⠀⠁⠛⣾⣀⠀⠀⠀⠀⣿⣿⣸⠉⠉⠚⠒⠒⠒⠒⠙⠟⠸⠀⠀⠀⡆⠻⠞⠴⠦⠺⠒⠓⠉⠈⣷⣿⣿⠀⠀⠀⡀⣄⢻⠛⠀⡀⢃⠈⠀⠁⠀ ⠀⠆⣽⡏⢸⠀⠀⠀⠀⠋⣿⣾⣠⢀⠋⠿⡿⣿⢿⠻⡟⣼⢀⠀⠀⠀⠀⡇⢻⠟⣿⣿⣿⠻⠈⣀⣦⣿⣿⠙⠀⠀⠀⠀⡇⣿⠀⠀⡇⢸⠀⠀⠀ ⠀⠀⣀⣿⠀⠀⠀⠉⡏⣻⣿⢺⠶⡶⣶⣤⣤⣠⣀⢀⠃⢰⠀⠀⠀⠀⠀⡆⠘⠀⡀⣀⣄⣤⣦⠶⠲⡟⣿⣟⠹⠈⠀⠀⡀⣿⠒⠀⠈⠀⠀⠘⠀ ⠀⠀⠀⡇⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⠀⠀⠀⠁⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⣿⠸⠀⢸⠀⠀⠀⠀ ⠇⠻⠈⣧⣿⣿⣶⣤⣀⣇⣿⠻⠈⠀⠀⠀⠁⠋⠞⣠⠀⠀⠀⠇⣠⢣⠀⠀⠀⡄⢷⠙⠈⠀⠀⠀⠁⠟⣿⣸⣀⣤⣶⣿⣿⣿⢀⠀⢫⠘⠀⠁⠟ ⡀⣸⠀⡇⣸⢀⠀⠀⠀⡇⣿⣿⣽⣯⣿⣤⣠⣧⠿⠿⠿⠿⠿⣸⠀⡀⢿⠿⠿⠿⠿⡿⣤⣤⣿⣽⣭⣿⣿⢸⠀⠀⠀⡀⣇⣴⠀⠀⣦⢠⠀⡆⢠ ⠀⠆⠛⡏⢻⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠹⠀⣿⣿⣿⣴⣤⣧⠀⠀⠀⡇⣤⣦⣿⣿⣿⠀⠃⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⡟⠙⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⠿⠿⡿⠀⠀⠀⡇⢿⠿⣿⣿⣿⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣀⣧⠀⠀⠀⡇⣠⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠘⠀⠀⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣀⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠞⣀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⣧⢘⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠦⠙⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠑⠀⠀⠀⠀⠀⠊⠈⠀⠁⠋⠉⠁⠉⠈⠀⠀⠀⠀⠉⠚⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢤⠓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠕⡿⠺⣟⣝⡝⡟⣿⣾⣿⣽⢘⠀⠉⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⡙⣤⣶⠥⠭⠶⣶⣐⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠉⠞⣤ ⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣤⣇⠁⠈⠀⠀⠀⠀⠀⡿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠁⠛⡴⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣾⢀⠀⠀⠀⡏⡸⢸⠀⠀⠀⠀⠁⣿⡈⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⠁⠞⣠⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠉⠖⡠⢋⡴⠀⠀⠀⠀⠁⣿⢸⢳⠈⠀⠀⠁⡿⣇⢻⠈⠀⣀⢤⠳⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠟⣰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠋⠟⠴⣠⢀⠀⠏⣠⠀⠀⠀⠀⠁⡾⣧⢸⠁⣋⣶⣷⡬⠀⣇⣸⢤⠑⠀⠀⠀⣄⣷⢿⠑⠀⠀⠀⠀⠀⠀⠏⣡⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣹⠀⠀⠀⠀⠃⢠⠀⠀⠀⠁⠜⣠⠁⡼⣄⣠⠀⠀⠀⣀⢤⡤⢧⠈⠀⢄⠐⠀⠀⡀⣳⣤⠒⠒⠒⠒⠤⣠⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢷⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⠋⡴⠀⠈⠖⣠⠀⠀⢄⠰⠀⠀⣆⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠦⡙⢤⠲⡖⠒⠒⠒⠙⠊⡴⢀⠕⣯⡿⢦⠙⠀⠁⠊⠴⡻⣿⣨⣀⢦⠙⠉⠁⠋⣷⠙⠉⠋⠞⣤⢉⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠓⢉⠉⠀⠀⣦⣸⣀⠀⠀⠟⣫⠛⣟⠀⡀⢤⣠⠀⠀⢹⠉⡈⢧⠈⠀⣀⣇⢸⠀⠀⡀⢀⠉⣚⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⢤⠶⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢦⣷⠘⠀⡟⣿⣯⢻⣿⠀⠀⠀⠀⠀⠀⣻⠟⣾⠸⢧⠀⠁⡽⠋⠶⠶⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢤⠲⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡟⣿⣻⣾⣷⣸⠀⠀⠀⠀⠀⠀⣷⣶⣷⣟⡿⢻⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠒⠤⠤⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠶⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⡶⣷⣦⣙⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠋⣠⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⣠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢣⠈⠀⠀⠀⠀⠀⠀⡇⠹⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⢁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡞⣠⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠆⣤⢤⠳⠉⠚⠒⠓⠙⠋⠖⠤⠤⠦⠿⣀⠀⠀⠀⠁⠉⠉⠚⠛⠖⡤⣀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠲⠛⠙⠉⠉⠀⠀⠀⠀⢰⠀⠂⠟⣖⣤⣗⠾⠙⠈⡄⠀⠋⠖⡤⣹⢀⠁⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⣸⡀⣀⢤⠦⠒⠖⡯⣦⠙⠈⠋⠔⣦⠘⣀⢤⣠⠀⠀⠀⣇⠛⣠⣀⣄⠦⠓⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠁⢰⠿⣾⣀⣦⢿⠐⣇⠈⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡟⣤⢀⠀⠀⠀⡀⢤⡤⢸⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠁⡞⢀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⡼⠀⠀⠀⠀⠋⡰⠀⠁⠊⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠋⣠⠀⠀⠂⠶⣲⠒⠴⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡷⠐⠀⠀⠀⠀⠀⠀⡗⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡄⠦⠻⠉⡟⣻⠀⠀⠇⠀⠠⠀⠀⠀⡁⣉⢀⡀⢅⢿⣿⣻⠀⠀⠀⣅⢹⣈⣀⣄⣤⣤⠶⣟⠰⡀⢸⠀⡀⢧⠈⠀⠀⠀⠀⣸⠋⣧⣗⠀⠀⠀⠀⣄⠽⠱⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⡿⣿⣿⠀⠀⡀⣁⠞⣡⣈⣒⢴⠥⣟⣿⣾⣴⣠⣀⣀⣀⣀⣀⣀⣃⣀⣧⠤⠳⠛⡉⠀⠀⢿⡄⣿⢾⣧⠘⠀⠀⡏⠇⢸⡇⡼⠀⠀⠀⠀⠀⣇⠸⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣿⣠⣇⠻⡘⢧⡈⢋⣴⠋⠟⡿⣾⣤⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣦⣷⣿⢿⣻⣯⠻⢈⢭⢹⠉⠞⢻⡏⢹⣼⢻⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠊⠀⠀⠀⠀ ⠀⠁⠞⣤⢀⠀⠀⠀⣧⠒⣀⢉⣄⣳⣤⣠⠀⠀⣆⢇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠴⠦⠛⡒⣶⣤⣤⣠⣀⢀⠀⠀⡇⢸⠀⠀⣄⣳⢇⠘⠀⠀⠀⡇⢰⠂⠠⠀⠀⠀⠀⠀⠀ ⠏⣾⠠⠀⠀⠀⠀⠀⠂⠁⢬⣷⠀⡄⢹⠀⠀⠀⠀⠀⣄⠑⠈⠀⠀⠀⠁⠉⠚⠴⣤⣀⠀⠀⡄⠱⠈⠀⠉⠉⠈⠀⠿⣰⡆⢸⠀⠀⠀⡀⢿⢹⠀⠀⠀⡾⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢀⠀⠀⠀⠀⠀⠀⠏⡿⢔⣤⠼⠠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⠴⣠⢀⠀⠀⠀⠀⠀⢃⠘⠋⣛⣒⢴⠳⠛⡴⣇⠛⠉⣀⠦⠙⠚⠔⣏⣤⢷⠙⡟⢀⡄⠹⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠋⡿⣾⢠⠀⠀⠃⠞⣀⠀⠀⠀⠀⠀⠁⠖⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣶⢒⠖⠶⡤⣀⢀⠀⡀⣄⣷⢿⠘⡀⢳⠀⣰⠀⠀⣄⢱⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠃⡵⢟⣿⢹⠀⠁⠟⣠⠀⠀⠀⠀⠁⠟⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢼⠀⡀⢸⠀⠀⠀⠀⡀⢧⠈⠀⡀⣶⠿⠙⠈⠀⠀ ⡆⠸⠁⠾⢋⡿⣿⣿⣿⠏⣿⢰⠁⠉⠉⠋⠾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⢈⠉⠘⠀⠐⠀⠀⠉⠀⠀⠀⢻⠼⣯⣿⠀⠀⠀⠀⠀⠀⣄⠛⠉⠈⡀⣤⡻⣬⠤ ⠀⢸⡏⡿⣿⣿⣿⣿⣿⣿⣶⠤⣤⣥⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢲⠒⠒⠓⠉⠈⠀⡀⢄⠁⡟⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⠀⠀⠀⣄⠳ ⠀⣅⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠤⠦⣷⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀ ⠃⡿⣿⣿⣴⣠⠀⠉⠛⠴⢀⠋⣴⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⣶⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀ ⣿⣾⣠⠀⠁⠞⡵⣼⢀⠉⠞⢠⠋⢸⠀⠀⠀⠁⠋⠒⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⣾⢀⠁⠟⣾⠤⣨⢁⡟⣴⠀⠏⣿⠀⠀⠀⠀⡦⠈⠀⠂⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀ ⢸⠃⣠⢀⠀⣿⠀⠏⢰⠁⡞⣧⣽⠃⡾⠛⠈⠁⠋⠛⠛⠙⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⢸⡆⠘⠀⠀⣄⣠⣟⠃⡼⢀⡇⣛⣿⠿⡿⣿⣾⣠⢀⠀⠀⡀⣤⢦⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀ ⢸⠀⢁⠈⠀⠁⣾⢿⣿⣿⠛⣸⣿⢀⣶⣿⣿⢻⠈⠀⠀⠀⠀⠋⠚⠒⡒⣉⣮⢶⠶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠋ ⣿⠈⡄⠻⠴⠀⣧⣿⣿⣿⣿⣿⣻⠀⠀⡀⣤⣷⣿⠻⠉⠟⣼⣾⣤⣤⣤⣤⣷⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠒⣶⣿⡿⣸ ⣿⢿⠙⠉⠋⠛⡿⣿⣿⣿⣿⣼⣷⢻⠈⠀⡄⢽⡲⣿⣿⣿⠿⢿⠿⠽⠭⠻⠙⣟⣿⠸⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠻⠚⠓⠙⠋⠛⠓⠈⠉⠀⣄⣱⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⢰⡄⣿⣿⠙⠀⡆⠹⠀⣀⣀⣤⣤⣦⣶⣿⣿⣿⣿⣿⣷⣾⣿⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠟⣻⣒⣖⣗⠳⠈⠀⠀⠀⢀⠷⠻⠍⣿⣼⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⡄⣿⢻⠉⣿⣿⣿⠹⠀⣿⠘⠀⠀⡀⠩⠤⠶⠒⠛⠙⡉⣈⣀⢥⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⠛⠻⠉⢧⣿⠸⠀⠀⠀⠀⣷⣿⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⣇⣿⣿⣿⣽⣧⣿⢻⣯⢿⠈⠀⠀⣧⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣴⠀⠀⠀⡀⣦⣿⣿⣿⣿⡟⣿⠙⠋⠛⠟⡾⣵⣯⣟⣿ ⣿⣿⣿⣿⣿⣼⣷⣿⣿⠀⡀⣿⣿⡏⢿⡀⣧⣿⣿⣿⢻⠀⠀⡂⢹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢠⠀⠀⠋⠱⡟⣿⣿⣹⣄⣤⣶⣷⣿⣿⣭⣠⣀⣃⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⡄⣷⣿⢸⠀⡄⣿⣿⣿⠀⡀⣷⣿⢾⣗⢿⠛⠉⣿⣄⠦⠒⠉⠉⠁⠞⢀⠀⠀⠀⠀⠀⠀⠀⠏⣾⢀⠁⠟⣿⢟⣿⣿⣿⣼⠀⣀⢤⠠⠁⡟⣠⣀⢀⠏⣿⣾⣯⣿ ⡄⣿⣿⣿⣿⣿⠀⡄⣿⢸⠀⠀⣧⣿⣿⠀⠀⡀⣷⢸⡀⣿⣷⣿⣿⢻⠙⠀⠀⣀⣄⢠⠀⠀⠀⠀⠀⠀⠀⠟⣾⢁⠟⣿⣿⣿⣿⣾⣡⡾⠀⠀⠀⠀⠁⡿⣼⠀⠁⡿⣿⣡⡿⣿⣿ ⠀⣇⣸⣧⣿⣿⠀⠀⣇⢸⠀⠀⡀⣿⣿⢸⠀⠀⡄⣿⠀⣧⠈⣧⣷⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠁⡟⣾⠏⣿⣿⣿⣿⣿⣴⢀⡟⢦⠀⠀⠤⠧⡿⣿⢛⡿⣿⣼⢁⡿⣿⣿⣿ ⠹⡀⣷⠀⣧⣿⠀⠀⡇⢸⠁⠀⠻⣇⣿⢸⠀⠀⠀⣧⠈⡀⢸⡏⡇⠀⣄⣦⣿⣻⢿⠿⠻⠀⠀⠀⠃⣴⡟⡿⣿⣿⣻⣿⣴⢀⠀⡏⣼⠀⠉⠋⠟⣿⣿⣵⣿⣾⣠⠃⣿⣿⣿⣴⢋ ⡄⠳⡎⠰⠀⣷⢹⠀⣿⠀⡇⢸⣧⡈⣿⢸⠀⠀⠘⡇⢸⠀⢧⣿⡇⠀⠀⠀⡀⣄⣷⣮⣿⣽⠹⠏⣰⡏⣿⣿⣿⣿⣴⢀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣣⢿⣿⣴⠀⠋⣿⣿⣾⣠⠏⣿ ⠘⡀⢧⠻⠀⡀⣿⠘⣿⠀⡇⢀⠀⢧⣏⢸⠀⠘⣇⠈⢠⠀⡇⣰⡇⠀⠀⠀⠀⠋⠴⢀⡁⣿⣿⢠⠏⣿⣿⣿⣴⢀⠀⠀⠁⡟⣿⣾⣵⣿⣿⣷⣿⣷⣿⣭⠬⠶⣷⣶⣠⠀⠇⣻⣿ ⡄⠰⡀⣦⠸⠀⡆⢹⣿⠈⡇⠀⠸⡀⣿⢸⣧⢀⠀⣿⡌⠀⡇⠘⡇⠀⠀⠃⡿⣼⠀⠏⣿⣿⢠⠇⣿⣾⢠⢀⠀⠀⠀⠁⡿⣿⢡⠟⣿⣴⢁⡾⢈⣦⠻⠄⣦⣷⣉⠀⠂⠁⡿⣿⣿ ⠀⠀⠀⠑⣇⠈⠀⣇⣿⢸⡀⠇⣷⠸⡆⢘⡇⠈⠻⡀⢇⠀⡟⢸⡿⠀⠟⣼⣟⢡⡿⣿⣿⢠⠁⡿⣴⠀⠀⠀⠀⠀⠋⣿⣿⢿⣿⣴⢀⠁⡾⢟⣦⠻⡈⣷⢮⠻⡈⣄⠷⣿⣿⣿⣿ ⠀⠀⠀⡄⢹⢿⠀⡄⣿⢻⠈⡇⡀⣷⠀⢸⡄⢸⣄⢰⠀⠇⣿⢻⣿⡟⣩⠟⢿⣿⣿⣿⣰⠋⣿⢩⠋⠛⠟⠷⣿⣿⣷⣿⣿⣾⣤⣠⣥⣾⠿⢲⠀⡀⣦⡙⣮⣿⣿⠻⠯⡿⣾⣤⠀ ⠀⠀⠀⠀⡆⡔⠠⠀⣿⣄⢳⡄⠀⡄⢺⢠⠀⢹⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣶⣶⣴⣩⢛⡿⣿⣿⣿⣿⣾⣠⠀⠀⠃⡴⡞⢠⠉⠛⠟⡿⣿⣿⣱⡟⣶⢸⣀⠀⠀⠀

⡀⣤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⢹⠆⡇⡿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⢻⣄⣷⣿⡻⣯⣿⣿⣿⣿⣿⣾⣀⠀⠀⡀⢷⠈⠀⣤⣷⣿⢿⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⡀⣿⣿⣿⣿⣿⢀⣏⣯⠘⠀⣯⣿⣷⣿⢿⠙⣄⣷⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⡄⠳⣌⠳⠈⠀⣄⣷⣿⢿⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢾⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣾⣸⣇⠃⣰⣀⢧⡟⣰⠀⠀⡀⣄⣷⢾⠈⣄⣷⣿⣽⢷⠉⠀⠀⠐⠀⠀⠀⣆⠹⣄⠱⠀⠀⣄⣷⣿⢿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⣦⢽⠳⠙⠈⠁⠉⠉⠚⠓⠶⠤⠥⣾⣴⣤⣦⢻⡾⣤⡿⣿⠘⠀⠀⣼⠀⠀⠀⠀⠀⡀⢻⠈⠆⠘⣄⣷⠿⣙⠀⠀⠀⠀⠀⠀⠀⡀⢦⡈⢦⠙⠀⠀⣄⣷⣿⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣝⣿⣈⢀⠀⠀⡀⢦⡟⣸⠀⠀⠀⠀⣷⢠⠀⢹⣄⢰⠀⡇⢸⠀⠀⠀⠀⠀⠀⡧⢰⠀⣀⢦⠙⣄⢷⠊⠀⠃⠈⠀⠀⠀⠀⠀⢇⠈⡀⢦⠙⠀⠀⣦⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣤⢦⣔⠀⠀⠉⠋⠟⣿⠛⠙⠱⠈⠀⡆⠐⠀⣠⠀⠀⠀⡆⢠⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡀⢦⠐⣄⠳⠈⣄⠳⠈⠀⠀⠀⠀⣄⠦⠙⡈⢦⠙⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠟⣾⣁⠋⠾⠀⠀⡀⣤⢦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠿⣙⠁⠁⠉⠀⠀⠀⡀⣜⠳⡈⢷⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠟⣶⣥⢿⣴⣠⠀⠀⠋⡰⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢻⠀⠀⠀⠀⠀⠉⠛⡟⠯⠿⠿⣐⣄⢦⣳⢮⠳⠉⠏⠿⠙⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⡼⣈⠏⣾⣞⠁⠛⠖⣿⢿⠴⠤⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⠦⠶⠽⣉⣋⡛⣛⣿⣿⣾⣿⠻⠈⠀⣄⠳⣎⣿⣧⣿⠹⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⢻⣾⠇⢿⣾⣡⡟⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣉⠋⠗⡿⣻⣿⣿⣿⣿⣿⠻⠈⡀⢠⡆⡿⣿⣿⠻⢀ ⠙⠀⠀⠀⠀⠀⠀⠇⢰⡏⠘⣷⢁⡿⣼⢋⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠞⠤⠭⣩⣈⠀⠀⠀⠀⠀⡀⣄⣴⣿⣻⣈⣔⣦⠛⠀⡄⡼⣷⣿⣼⠻ ⣄⢦⠛⠈⠀⠀⠀⡇⠀⡇⣼⡀⡇⣰⠇⣰⠀⠀⠉⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠿⠤⣼⠃⡿⣿⣾⢠⠀⠀⠀⠀⠀⠁⠿⠿⣷⣱⣷⢬⠳⠈⣇⣼⣇⡈⣷⣿⡏ ⠀⠀⡀⣤⢶⠙⠈⡄⠀⡄⢹⠀⡀⠀⣧⢯⡾⣡⣟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⡆⣛⢷⢹⡄⣤⣠⠀⠀⠀⠀⠀⠀⠀⣧⣴⢸⡇⡜⡀⢷⠈⣀⣾⢎⡀⢳⡈⣷⢸ ⠉⠀⠀⠀⠀⠀⣀⣮⠿⠿⣿⠙⠈⠀⠀⣀⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠏⣿⣧⣏⠘⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⠀⢹⡀⢹⢣⡀⢣⠀⢸⣆⠙⠧⣏⡘⢻ ⣛⣉⢭⠉⠉⠋⠾⢶⣤⣃⣿⢀⣄⢤⠷⡿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⠁⣷⣷⠸⢻⣿⠈⠀⠀⠃⠛⠿⠰⣟⠘⣿⠀⡆⠘⡆⠘⢣⠀⠀⢸⠁⡄⡿⡹⣇⡀ ⣿⣿⣾⣠⣉⠛⠐⠀⠟⣾⢀⠀⠀⠀⣼⣿⢲⠐⠁⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠃⢰⣧⡗⡼⡽⢻⣀⣧⢳⠁⡽⣿⣶⣡⠞⣷⢠⢻⠀⡄⢆⠀⢀⠈⠂⠀⡇⠀⠀⣇⣫⢿⠁ ⡯⣿⢋⠟⣿⣰⠁⡿⣴⠀⠀⠀⠀⡇⢻⡟⠻⠈⠀⠀⠀⠀⣀⣄⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⣦⣿⡄⣿⠸⡎⡘⣷⣾⢀⠀⣠⠀⣷⠘⡄⢳⠈⠀⠀⠀⡄⠱⠀⡀⢸⠀⡈⣿⣜⠀ ⠀⡀⢧⡎⢀⠁⡛⣠⠀⠀⠀⠀⠀⡇⣾⣶⣿⢿⠙⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⡄⠰⠁⢺⡟⣿⢾⠷⠛⠛⡉⢧⠈⠀⢤⠤⠲⡓⢈⠀⠀⠀⠀⠛⢧⡇⢻⠀ ⠀⠀⠀⣀⠀⡿⣠⠀⠀⠀⠀⠃⡾⣟⠀⠀⠀⡀⣤⢿⠙⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢻⡖⣰⠀⠒⠓⣉⢌⡠⣖⣤⣄⢦⠙⠁⠉⠀⠀⣄⢦⠙⠀⠀⣿⡇⡏⣤⢇ ⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠆⣰⠏⢰⠀⠀⠀⠀⠀⡀⣄⢶⠺⠙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡧⢿⣟⣿⢿⢜⣌⠳⠛⠈⣀⣤⠲⠙⠀⠀⡎⠳⣹⠀⠀⠀⠀⡀⢧⠙⣏⡿⣾⠙⡗ ⠀⠀⠀⠀⠀⠀⣅⠾⡤⠦⠛⡸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠲⠀⠀⠀⠀⠀⠋⠖⣠⡀⢷⣝⣷⣽⣿⠻⠈⣄⣦⢿⠳⠙⡙⣄⠢⠖⢩⡈⣄⠦⠑⠉⠀⠁⣿⣿⢀⠃⣼⡇ ⠀⠀⠀⠀⠀⡖⢀⠀⠀⠀⡀⢦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⣀⠀⠀⠀⠀⠄⣲⣖⡷⣿⣿⣶⢿⠛⡉⠘⢠⡀⣦⠽⠬⠓⡚⣒⣖⠲⡷⣼⣀⢟⣾⠞⣰⠞⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣻⣿⢶⡿⣿⣿⣟⠿⡙⢀⢀⣹⢀⣴⢁⠂⠑⡉⣏⡴⣁⠋⣵⢋⡿⣴ ⠀⠞⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣤⣠⢀⣇⠻⡞⣷⣿⣿⣿⢿⡺⣶⣛⣿⢿⠿⣿⣿⣽⠭⠭⡉⣋⠟⣴⢀⠀⠀

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⠀⠀⠀⠀⠀⠀⣀⢄⠤⠶⠲⠒⠙⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠒⠒⠴⠤⠠⣀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡀⣀⣀⣄⣤⣤⠤⠤⠤⠦⠶⠒⠺⠀⠒⠒⠿⠀⠀⠀⠀⠀⠃⠚⠖⠴⠥⠭⠭⡮⣶⣴⣒⣀⠁⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⢄⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⢻⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⠀⡄⢀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⡀⠳⠈⠀⠁⠞⡴⣀⠀⠀⠀⠀⠀⡀⣄⠶⣝⠻⠀⠀⠀⠀⠁⣼⠈⠈⠀⠀⠀⠀⠀⠉⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⣀⣀⠀⠀⠀⣀⣀⢤⠳⠉⠀⠀⠀⣀⠯⣰⠀⠀⠀⠀⠀⠉⠚⠒⠒⠐⠂⡙⣦⢿⠈⠋⠟⣶⣶⢶⡲⣓⠿⠻⠚⡴⢀⠀⠀⠀⠀⠀⠁⠉⠋⠒⠒⠒⠒⠛⠈⠀⠀ ⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢾⠒⠛⠋⣰⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣰⠀⠉⠚⠤⣠⡀⣀⣄⠢⠙⠀⠀⠀⠁⠚⡴⣀⠀⠀⠀⠋⡰⠀⠀⣆⠙⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⣧⢻⠉⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢾⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠃⡰⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⣄⠘ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣆⠹⠀⠀⡀⢻⣀⢤⠶⠲⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⡼⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠦⠈⠀⠀⠀⠀⠀⠏⡻⣶⣸⠀⡀⣦⠳⠙⣯⠀⠀⠘⠀⠀⣀⣀⢤⠶⠶⠒⠛⠉⠉⡏⢸⠀⡄⠷⠙⠈⠀⠀⠀⠀⠀⠀⡿⣟⣾⠤⠷⠈⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⢀ ⠀⠀⠀⣄⠣⠙⠀⠀⠀⣿⢠⠀⣧⠈⠀⠀⠀⣥⣿⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⢤⠤⠤⠦⠒⠒⠒⡒⣿⣸⠀⠀⡇⢸⠄⢸⠀⠀⠀⠀⠀⠀⠟⣠⠀ ⠀⠀⠀⠀⠀⡆⣿⢤⠤⣧⠘⠀⡀⣄⠿⠤⡤⣀⠋⡴⢠⠀⠀⠀⠀⠁⠉⠛⠒⠒⠒⠒⠔⠿⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠏⣰⡄⡿⢿⠙⠀⠀⠀⠋⡶⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣳⠈⠀⣄⠻⠉⠁⡾⠀⠋⡴⢀⠀⠀⠀⠀⠁⠟⣴⣀⢀⠀⠀⠀⠀⠁⢰⠀⠀⣀⢧⠳⠉⠀⠀⠀⠀⠀⡇⣷⠛⡴⢀⠀⠀⡏⣸⣄⠷⠛⠾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⣇⣌⣴⢀⠟⣠⠀⠀⠀⠀⠀⠛⡴⢀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠋⠴⣀⠀⡀⣄⠳⠈⠀⠀⡀⣦⢙⠉⠀⠁⠋⣷⣸⠀⡇⣾⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⡆⢻⠀⡇⢸⠀⠀⠀⠁⠞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠟⣷⣸⠀⠇⢸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⡀⣀⣃⣿⢀⠀⠏⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⣧⠘⡉⠙⠋⠖⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣰⠀⢿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⣄⠻⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣞⣹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣼⠀⠀⣿⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡀⢦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⢸⠀⠀⡀⢷⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⡀⣄⣤⣦⢿⣤⣤⣤⡀⣿⣸⣧⠸⠀⠀⠀⡀⣷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢦⠙⠈⠀⠀⠁⡍⢺⠒⠒⠒⣟⢻⡙⣄⠤⠤⠢⠒⠒⣿⢯⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⡵⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣋⣞⣶⢳⠙⠀⠀⠀⡏⣿⣿⢩⠉⠉⠉⠉⠏⣿⣿⢀⣆⣤⠷⠾⠻⠚⠗⠿⡿⣩⢖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⡽⢓⠀⠀⠀⣆⠛⠴⣠⣀⣦⣳⣭⣬⣤⣭⣿⣿⣼⢀⠀⠀⠀⠀⣄⣳⠈⠄⣻⢧⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⣤⢤⡀⣷⢻⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⣋⣴⣤⣏⣠⠀⠀⠉⠚⠐⠀⠀⠀⣎⠻⣿⣼⣒⣀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡉⢿⠙⠀⠀⠀⣷⢹⠛⣿⠉⠉⠉⠉⠀⠀⡎⢠⠋⡶⢀⠁⠎⡴⣀⠀⠀⠀⠀⠀⠀⡀⣷⠺⠀⠀⡏⢹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣽⠋⠚⠖⠴⡤⣠⢦⠳⠛⢟⣶⣷⢿⠿⠯⠶⣛⣌⠷⠉⠞⣠⠋⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣤⣀⣁⣉⣙⣍⠯⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠟⣿⢠⠁⡿⣿⣿⣿⢾⡤⢳⡏⣴⢋⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠗⠀⣀⠀⠀⠀⡀⣇⣿⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢦⠹⠀⠀⠀⠉⠛⣟⣿⡿⣿⣿⢙⡉⣿⣿⣿⣿⣿⢿⣼⢡⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠸⠀⠀⠀⠀⠀⠋⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠿⢿⣒⣒⣟⣿⣿⣶⣶⣶⣶⣶⣷⣿⣾⢠⠃⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠉⠋⠚⠖⣤⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡴⣀⢀⠉⠞⣤⣀⠀⠀⠀⠀⠀⠁⡟⣴⢀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢘⡑⣄⠦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠏⣴⢀⠁⠞⡴⣀⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢸⠀⣄⣤⡳⣿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢰⠀⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢠⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢠⠀⠀⠀⠀⣄⣿⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣱⢋⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠸⠀⠀⠉⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⣠⠀⠉⠖⣠⠀⠀⠀⠀⠁⠟⣼⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⢀⠀⠀⠀⡀⢦⠙⠀⡀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⢰⠀⡤⢀⠀⠈⠀⠁⠋⠴⣠⠀⣄⠳⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⣀⢦⠙⠀⠙⠀⠀⠀⡀⠣⠘⡇⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣤⠤⠶⠒⠒⠴⠤⣤⣀⠀⠀⠀⠀⠀⠀⣄⠦⠙⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣠⠀⠀⠀⠀⡀⣄⢦⡒⢻⠛⠛⠛⠛⡾⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠲⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠂⠔⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠆⢿⢈⠀⠀⡀⣀⣀⣄⢠⠀⠀⠀⠀⠀⠄⢠⠀⠋⡖⣠⡀⡏⣿⣉⠶⠛⠈⠀⠀⠀⠀⠀⣄⠲⠙⠀⠀⣄⣦⠙⠀⠀⠀⣀⢷⠈⠀⠄⠈⠀⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢧⠉⠈⠀⠀⠀⠀⠀⠃⠈⠀⠆⠙⠀⠂⡴⢀⠁⠞⡤⢀⡏⣻⣯⠷⢛⠈⠀⠀⠀⠀⠀⠀⡀⠄⠶⠿⠿⡛⢿⠛⠉⠈⠀⣦⠙⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣧⣜⠦⠶⠶⠶⡶⣑⣭⠻⠉⡀⢷⠀⠀⠞⣠⠀⠃⠞⣳⣿⣵⣛⣉⣤⠷⠿⠿⠶⠶⠶⠲⠒⠙⡈⣦⡹⣄⣷⣿⣿⠻⠈⣆⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠶⣝⠻⠈⠀⠀⠀⠀⡀⢦⣙⢬⠶⠛⠉⠁⠋⡾⣠⢋⡾⢂⡾⣿⣿⢿⠿⠉⣁⠈⠀⠀⠀⠀⠀⣄⢷⣟⢻⠀⣧⣿⣿⢿⠈⡄⢷⣏⠈⡄⠹⠀⡀⢳⠈ ⠀⠀⠀⠀⠀⡀⢤⠶⠙⡉⣈⣦⠿⠙⠀⠀⠀⠀⡀⣄⠦⠲⣙⣯⣻⠛⡾⣠⠀⡁⠟⣴⣀⣿⣠⣄⣦⣿⣹⢬⠦⠲⠓⠉⠈⡆⣷⠸⠀⣧⣿⣿⢺⠈⡄⣿⢰⠈⡀⢣⠈⡀⢦ ⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣶⣾⣶⣷⣿⠻⠉⠀⠀⠀⠀⠀⠀⣅⣿⣠⠀⠀⠃⣼⢀⠁⡞⣠⠀⠀⠀⣄⣷⢿⠀⠀⠀⡀⣄⢷⣿⣿⠘⡀⣿⣿⢿⢻⠛⡿⣼⣤⣤⣦⣤⢤⠷ ⠀⠀⠀⠀⡀⣃⣿⣴⣤⣤⢦⠒⠓⠀⣀⣄⣷⢿⠛⠀⠀⠀⠀⡇⣼⠀⠀⠀⡟⠙⠟⣠⠀⠀⢧⠙⠛⠙⠛⣿⢠⠀⠀⠀⠀⠀⣷⣿⢠⠀⡇⣿⣿⣼⢀⡆⠰⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣇⣿⢷⠛⣷⠈⡟⢸⠀⠀⠁⣿⣿⢠⠀⠀⠀⣧⣾⣥⣯⣾⣠⠀⠀⠀⠀⠀⠀⡀⣷⠸⠀⡇⣿⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿⡇⣼⣷⢿⣿⠘⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⣄⣡⢀⠀⠀⠀⠀⠀⠀⠀⠛⠉⡏⢹⠀⡇⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢻⡇⣿⣿⢻⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀⣤⢠⠀⠀⠁⠼⣤⣠⣀⢀⠀⣏⣿⢀⡇⣿⣿⣿⣷⢿⠛⠙⠉⠈⠁⠉⠁ ⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠀⣦⣿⣿⣿⣿⠈⠀⡄⣿⣿⢸⠛⠴⣤⣤⣤⠻⠀⠀⠀⡷⠉⠛⠿⠻⠞⣴⣧⢿⢀⡇⣿⣿⣿⡇⣿⣾⣿⣾⣿⣿⢸⠃ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠙⠟⣾⣆⢻⣦⢻⠀⠀⡇⣿⣿⢹⠉⠿⣿⢞⣠⠀⠀⠀⠀⢛⣛⠒⠐⠀⠀⣿⣿⠀⡇⣻⣿⣹⡇⣿⢸⣟⢿⡟⣿⣿⣠ ⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢀⠀⣦⠛⣧⠹⠀⠀⣿⡻⣀⣀⢒⠄⠤⠠⠀⠀⠀⠀⠁⠋⠛⠚⠐⠀⣇⣸⠀⡆⣧⣿⢠⡇⣿⢃⣿⣆⢿⣿⢧⠘ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠘⠀⠀⡇⣴⠘⠀⠀⣦⢻⣷⠙⠀⣆⣿⢻⠁⠋⠛⠛⠙⠈⠀⠀⠟⣶⣤⣀⠀⠀⠃⣿⢸⠀⠁⣿⢸⠀⣿⢰⠀⠉⠟⣿⢸⡄⢻ ⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠀⠀⠀⡏⠻⢀⠀⠀⠀⣄⣿⣷⠹⠀⡀⣷⣿⣽⣳⣿⣛⣈⢦⠿⡛⢯⠙⠀⠀⠁⣿⣾⢀⠀⡟⣸⠀⡇⣿⠛⡾⣤⢀⡏⢰⠀⣠ ⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠏⣼⡀⢷⠘⠀⠀⠀⡀⣷⣿⠻⠀⠀⣄⣷⣿⣿⣻⣦⠻⣯⣿⣿⢿⠈⠁⣿⣿⢰⠀⡇⣽⠉⠟⡾⣠⢀⠀⠁⠏⣸⠀⠀⠿ ⠀⠀⡇⢼⠀⠀⠀⠁⠉⠉⠚⠖⠶⣿⣤⠦⠤⡿⣰⠀⠀⠀⣦⠻⠈⠀⠀⠀⣦⣿⢿⠙⠀⠀⣀⣀⣦⠹⡀⣷⣿⣼⡀⣦⡿⣿⣰⠁⠋⣿⣾⣤⣀⠀⠀⠀⠁⡟⣿⢻⠀⠀⣾ ⠀⠀⡇⣿⠋⠾⣤⣠⣸⠀⠀⠁⠉⣿⠀⠁⠞⣠⠀⠀⠀⠀⠋⠀⣀⠀⠀⠀⠀⡀⣶⣿⠻⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⡏⣿⣿⡶⣴⣀⢀⠀⠀⠀⠀⠀⠏⣴⣏⣿⣾⠀⠃⢿ ⠀⠀⡀⣾⣀⠀⠀⠏⢺⠗⠼⣠⣞⣼⠁⡾⢀⠀⠀⠀⠀⠏⣸⠀⠀⠀⠀⢦⠻⠈⠀⣇⣮⢶⠙⠉⠉⠉⠉⠉⠉⠉⠟⣶⣤⢀⠀⠀⠀⠀⠀⠀⠁⠋⡶⣡⠟⣰⡇⢰⠁⡟⢸ ⠀⠀⠀⢡⠛⠀⡇⣠⠃⣸⠀⡞⢀⢧⣼⠀⠀⠀⠉⠟⡶⣠⠀⠀⠀⠀⠀⠀⡀⣄⠶⡶⢙⠀⠀⣀⣀⣒⣀⣂⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⢋⠞⣴⢀⠇⣰⠁⡟⣠⢀ ⠀⠀⠀⡄⣇⠸⡄⠀⡜⠀⡞⢠⠃⡿⢺⠀⠊⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠶⣤⢀⠀⣀⠀⠀⠀⠀⠁⡿⢸⠀⠁ ⠀⠀⠀⠀⡇⢸⠰⠂⠰⠆⢠⠀⣧⣸⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣄⠦⠙⠉⠉⠉⠉⠉⠛⠛⠶⡴⣀⠀⠀⠀⠀⠀⠉⠈⠁⠋⠾⣿⣸⠀⠀⠀ ⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⡄⢲⠉⣏⣿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠓⠉⠩⠀⠀⠀⠀⠀⣀⣉⣯⣶⠛⠉⠉⠈⠀⠀⠀⠀⠀⠋⡿⣾⣴⣠⢧⠛⣼⠀⠀⠀⡀ ⠀⠀⠀⠏⠿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⣷⣌⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠒⠶⡤⣀⢀⠀⡿⡴⣈⣄⢤⠤⠤⠧⣽⣀⣄⢶⠻⠈⠀⣏⢸⠀⠀⠀⠀ ⠀⠀⠃⣿⣿⢿⠙⠀⠀⠀⠀⠀⠉⠞⡴⣀⠀⠀⣀⠶⡙⣉⢤⠶⠶⠒⠛⠒⠒⣿⠞⠶⡶⣠⣀⠀⠀⠉⠋⠶⡤⣀⣟⣤⣳⢬⠳⠯⠈⡆⣄⢸⠀⠀⡀⣄⣾⣼⢣⠀⠀⠀⡽ ⠀⠃⣿⣿⣼⣶⣿⢿⠿⠿⡾⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠶⠒⠉⠉⠉⠉⣯⠉⠉⠉⠉⠚⠶⡤⣀⠀⠀⠀⠀⣿⠈⠀⢿⠀⣧⣦⢻⠈⣇⠀⠀⠃⡿⣿⢰⡀⢀⠀⡀⣀ ⠃⣿⣿⣿⢹⠛⠿⣻⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣟⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⢻⠀⣇⠀⡇⠀⡇⢰⡇⠀⠏⣰⣏⢰⠀⠀⠀⠀⠀⠀ ⡆⣿⣼⠀⣏⣿⣾⣧⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⢯⠙⠈⠀⠀⠏⣠⠀⡀⠀⡆⠀⡄⠀⡟⡼⢁⡟⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⢻⡟⣿⣽⠛⢳⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠹⠀⣄⠶⠟⣴⠀⠀⠀⠀⠀⠀⠐⡇⣻⠟⣴⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣀⣀⠀⠀⡏⠼⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⣤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⢸⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⡴⢀⠀⠀⠀⠀⣁⣭⠿⠛⠛⠛⠛⠛⠛⠛⡿⣷⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠛⠛⠛⠟⣿⣽⣧⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣸⠀⠁⡋⠟⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠳⣟⣿⢿⠛⠙⠉⠀⠀⠁⠋⠛⠛⠛⠛⠉⠉⡟⡶⣿⣿⢬⢃⡿⢛⡟⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⡙⢂⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣀⣦⠧⣿⣿⣤⠀⠀⠉⠉⡈⣤⣶⠙⠀⠀⡄⣿⣧⢿⣷⣼⣠⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣶⢷⠙⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⣿⣰⠀⠄⣤⣀⢀⠀⠀⠀⠀⡀⣄⣤⠦⣿⠻⣷⣿⢹⠀⣿⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠴⣤⣃⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣇⣤⣦⣿⣿⣿⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠋⠴⣠⢀⠃⠀⠀⣾⠁⠛⠟⢿⠾⠶⠶⠛⠙⠀⠀⠀⠋⠟⣾⢿⣿⡛⠙⡟⣾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⢀⠀⠀⠀⡇⠁⡿⢿⣿⣿⣿⣿⣷⢿⡷⣿⣿⢿⠟⣿⣿⣿⣿⢉⣟⣿⣿⣿⢠⣼⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡟⣼⣟⣿⣿⣿⣼⡏⠉⢟⣿⣿⣿⣿⣿⣿⣿⣄⣿⣠⣿⣾⣏⣌⡇⢿⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⠃⣿⢀⣳⢸⡇⣇⢰⣼⢿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠼⣿⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠁⠋⣾⢁⠟⣰⠀⣸⡄⠀⣿⣹⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣟⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣷⣿⢉⣿⢸⡟⣄⢋⡿⣰⠀⡆⢀⠘⠀⣌⡁⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⡿⣿⣿⣿⠟⣸⡶⣆⣠⠀⠀⠀⠇⢰⠀⠁⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠃⣿⣟⣯⣶⣶⠰⠀⠁⠋⠚⡶⢀⠀⠀⣀⣥⡈⣄⣦⣛⣖⣮⠶⠿⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠐⠄⠤⠤⠤⣨⣛⢉⠈⠀⠀⡀⣤⠦⠓⣛⣌⣦⣷⢴⢤⠤⠤ ⠀⠀⠀⠀⠀⠀⠁⡾⡀⣦⣶⣴⣤⣠⣧⣨⠀⠀⠀⠀⠉⠛⠿⣿⢿⠿⠿⠿⠙⠈⠀⡄⣿⣿⣿⣻⣛⣝⣩⣭⣿⣻⠉⠀⠀⠀⠀⢳⣆⣘⣀⣤⠷⠳⠙⠈⠀⠀⣀⣄⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⣿⣾⠮⠳⣌⠧⠙⠉⡟⠀⠀⠁⠏⡿⣿⣴⣀⣀⠀⠀⠀⠀⠀⡀⣄⠦⡓⣭⣿⢸⠀⡀⣀⣀⣄⣦⣿⣶⠳⠙⠈⡆⠘⢆⠙⠈⠀⢰⠀⣀⢦⠳⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⡞⣷⣿⢀⢳⠐⡀⢧⡙⣄⣷⠀⠏⡿⣝⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣵⠹⠀⡀⢹⠀⢧⠉⡄⣿⢿⠟⠻⠉⠀⠀⡀⢀⠀⠀⠂⠀⠀ ⠀⠋⡾⣤⠂⡟⣸⠀⡸⠀⠁⡽⣹⢤⠲⠗⣿⡿⣾⢢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣌⠘⠀⡆⠸⠀⣧⣤⣦⣿⣿⣹⣷⢾⠻⠙⠀⠀⠀⠀⠀⠀ ⡀⡃⢿⠀⠆⢧⢠⠇⢀⠀⡻⡸⣿⠉⢸⡏⣿⣴⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠸⠀⢧⠡⠀⢧⠈⠀⣄⣷⡜⣳⡝⣿⣿⠻⠙⠀⠀⠀ ⠐⡿⣸⠀⠃⣷⢿⣸⠀⡏⡼⠀⣧⣿⠠⣿⣰⠤⠲⠽⠤⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢦⠙⠀⠀⠀⠀⠀⠀⠀⡀⠸⡄⠘⡀⡽⠱⠀⢆⠙⠀⠀⢇⡘⣷⣠⣀⣄⣤⢶⠙⠀ ⡯⣿⢸⠀⠠⠀⣿⢀⠃⢹⢰⠀⡄⣿⠋⢰⠀⠀⠀⡀⢦⢧⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠟⣿⢳⠀⠀⠀⠀⠀⠀⠀⡆⠘⡄⠱⣇⡹⠀⠀⡄⠳⠀⠀⣆⡈⢳⠋⠜⣠⠀⠀⣀ ⣿⣿⢻⠠⠀⠀⣽⠀⡎⡇⠀⠘⠀⣿⣠⠀⠀⠀⠀⠀⠀⡏⣿⠘⠉⠀⠀⠀⠉⠉⠋⠘⣿⣿⣿⣿⡿⢿⠈⠀⠀⠀⠀⠀⠀⣆⠈⡁⣧⣿⠻⠀⠀⡀⣄⠙⠀⣧⠘⣧⢹⠀⠀⠀⡀ ⣿⣶⢠⠁⠀⠀⣾⠀⢸⠀⠀⢻⡏⣰⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣻⣾⣣⢻⠀⠀⠀⠀⠀⠀⠀⢧⡘⠀⣄⣷⢳⠀⠀⠀⡀⢤⠙⢇⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⣸⠇⠀⢠⠇⢀⢸⠁⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⢾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠄⡙⣦⢿⠙⠀⠀⠄⡑⣯⣿⡜⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⡇⠁⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⢀⣏⣷⣾⣿⣿⣿⣻⣶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡀⢦⣐⡄⢱⠀⠀⡀⣄⣦⢸⠀⠀⠀⠐ ⠀⠀⠀⠀⢀⠁⠀⡇⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢴⠶⠴⡤⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⠈⡄⠑⡄⠳⠈⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣵⠳⠈⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣼⠳⠉⠉⡉⢿⠙⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠘⠀⠀⢠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠤⣤⠻⣏⣿⣿⣴⣀⠳⠀⠀⠀⠀ ⠀⣇⠙⠉⠀⠀⢸⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠐⠋⠚⠽⠋⠟⡿⢶⣿⣿⢞⠐⠀⠀⢀⠀⠀⠀ ⠈⡄⣼⡶⠛⠉⢹⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⣤⣫⣿⣿⣾⣿⣯⣶⣤⣁⠋⡿⣴⣠⠀⠀⠁⠋⠒⠀⠀⠀ ⢳⠸⣇⠈⠀⣄⣧⠈⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⣻⣟⣶⣿⣉⠛⠾⣶⣤⣋⠔⠤⠤⡥⣭⣋⠒⠓⠘⠀⠀ ⡇⢯⠈⣷⠻⠙⡄⢸⠘⠀⡇⣇⣿⢻⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠄⠷⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⣶⣤⣤⣭⣤⣠⣀⠀⠀⠀⠀⢲⠛⠖⠤⣗⣘⣆⠘⠎⢀⠀⠀ ⠉⣹⢳⡀⣾⣿⢿⣟⢸⠀⡇⡀⣿⣿⠉⡿⠀⠀⣷⠛⠟⠿⠿⠻⠗⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⡄⢷⠈⡀⠹⠀⡈⢷⠈⣞⢀⠀⠉⠈ ⡀⣧⡜⠙⡆⢿⣷⣿⣏⠘⡇⢸⣆⣿⣿⣶⢿⠿⡿⣿⣾⣤⡤⣩⣏⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠹⡄⠸⠀⡄⣿⢠⠁⡼⢀⠀ ⠀⠀⢧⣆⠘⣆⡘⢻⣸⢳⡇⢸⠀⣧⣿⣦⣽⣤⣤⣤⣤⣤⣤⣀⡄⠻⠀⠀⠢⠙⠀⠀⠀⠀⠀⠀⠀⡄⢷⠙⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⣏⠀⠃⣰⠁⡼⡀⠐⠀ ⠘⠀⡀⢳⢧⠀⢃⡄⢻⡄⡜⣿⠀⠀⣧⠸⣄⠓⠀⠀⠀⠀⠀⠀⢱⡀⢳⠈⠈⡀⣄⠳⠛⠈⠀⠀⠀⠀⡀⣷⠫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣯⢿⣠⠀⡟⠀⠀⠀⠈ ⣿⠘⠀⡀⣳⢷⡄⠘⣇⠸⢆⣟⢹⠀⠀⣧⠘⡀⢦⠙⠀⠀⠁⠉⡏⠘⡀⣧⠈⠀⠀⠀⣄⣧⠾⠙⠀⠀⠀⠀⢧⢮⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠏⢠⠀⠀⠀⢁ ⣧⣿⠹⠀⡀⡹⢳⠁⠀⢧⠀⣆⡞⠘⣀⢤⢷⠙⠈⡀⣦⣙⢀⠀⠀⣦⠈⠀⢆⠘⠀⠀⠀⠀⣀⡳⢮⠙⠀⠀⠀⣦⡌⠳⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣤⢾⢠⠃⡸⠀⠀⠀⠀⠀⡀ ⡄⣶⣿⢿⠙⡀⣱⣧⠘⡀⢸⠀⣆⢯⠀⠀⠀⢱⣄⡶⠽⡚⢯⠈⠀⠀⢧⠈⠀⡄⠳⠀⠀⠀⠀⠀⡀⡣⢮⠙⠀⠀⢇⡈⢳⠈⠖⠶⠴⡤⣠⣀⠀⠁⡼⠀⠏⣠⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣷⢿⡙⢣⢯⠈⡆⠘⠀⢦⢿⠀⠀⡀⢱⠀⠀⣄⢦⣕⠺⠙⠈⢣⠀⠀⡀⢦⠙⠁⠀⠀⠀⠀⣄⡳⢮⠙⠀⢧⠈⢧⠈⠀⠀⠀⠀⠀⠋⣰⠀⠞⢀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣤⢷⣿⢫⠀⢆⠈⠀⣆⢻⠀⠀⡀⠱⠀⠀⠀⠀⣄⡳⣌⣦⠻⠀⠁⠋⡀⠳⣌⠓⠈⠀⠀⠀⢄⡙⠢⠈⢳⠀⢧⠈⠀⠀⠁⡴⢀⠀⡏⢀⠀⠀⡄⢸⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⡀⣄⠹⠀⣦⠈⠀⣄⢿⠈⠀⡄⠳⠀⠀⠒⠓⠛⡚⠲⡽⣷⣃⠈⠀⡀⣦⠻⢌⠑⠀⠀⠂⡈⠣⡌⣷⢹⠀⢧⠁⠞⣠⠀⠀⡎⢠⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⠀⠐⠈⠀⠀⡄⢱⠀⢇⠘⠀⡀⢷⠘⠀⡀⢣⠈⠀⠀⠀⠀⠀⡀⢤⢷⢎⠙⠀⠀⡄⣷⠻⢌⠐⠀⣄⠰⢦⡈⣧⠘⠋⣰⠀⠀⠁⠞⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠑⠈⠀⡀⢦⠑⠈⡄⠻⠀⣄⠘⠀⠀⣆⠘⠀⠀⢆⠙⠀⠀⠀⠀⠀⠀⠀⣆⡝⠳⠀⠀⠀⣆⣿⠓⠈⠀⠀⠀⡆⠙⣼⢀⠀⠀⠋⡰⠀⠀⠀⠀⠋⠟⡿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠲⠉⠀⠀⣀⢤⡖⠻⠈⡄⠱⠀⠀⡀⠢⠈⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⡄⠱⢆⠙⠀⠀⡀⣶⣭⠷⠛⠞⡴⣠⠀⠁⠛⡼⢛⠛⠻⠾⠿⣷⣵⢸⣏⣿⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣿⡌⣥⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⡀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣀⣀⣀ ⠄⠀⠀⠀⠀⠇⣾⣦⠰⣀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠞⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⣀ ⠈⠂⠀⠀⠀⡀⣤⣳⣿⣉⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣶⠿⢰⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣀⣸⢤ ⣀⠀⠀⠀⣾⣧⠰⡟⣾⣶⣷⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⡃⣿⣿⣿⣿⣿⣿⣶⣿⣿⢶⠶⠤⠥⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⢀⠀⠇⢠⡸⠀⣶⠽⠿⠟⡛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⣿⣿⣶⣿⣴⣡⠟⣾⣠⢀⠀⠃⢞⣠⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⡼⡏⢉⠞⡤⣉⠟⣭⣉⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⢋⡴⢀⠃⡿⣴⠀⠀⠀⠄⣠⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏ ⠀⠀⠏⢰⣠⢉⠖⣥⢈⣧⣿⢀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡴⢀⠀⡴⢀⠀⠃⣣⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣟⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠴⣀⠋⠖⣠⢀⠀⡼⣀⣇⢸⠀⠀⡅⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⣠⠀⠀⠀⠀⠀⠀⠀⣹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣷⣹⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣀⠀⠀⠀⠀⡞⢀⠁⣿⣿⣶⣒⣒⣗⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢀⠀⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣤⢶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⡼⠀⣌⠉⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠸⠀⡆⠘⠀⢷⠀⠀⠀⠁⠀⠁⡟⣶⠤⣤⣤⣤⢤⠲⠀⠀⠀⠀⠀⠀⠁⠚⡴ ⠀⠀⠀⠀⠃⣰⠀⡞⢀⠀⢿⣴⣀⣿⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠘⠀⢡⠀⡀⢻⠉⠟⢼⡤⣀⣄⠤⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣡⠞⡴ ⡞⣄⠳⠙⡼⠀⠏⢠⠀⠁⣼⠀⡏⢠⠀⠀⠀⢦⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠻⠉⣟⠾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠃⣰⠟⣠⡀⠀ ⠀⠁⡼⣞⠀⠀⢶⠓⠉⡼⠀⠃⣰⠀⠇⠾⠒⠙⣄⢹⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠾⡠⢇⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⡸⠇⢀⠀⠀⠀ ⠁⡿⡴⢿⠛⠉⠈⠀⠀⢀⠁⡿⠙⠚⠉⣈⠣⡌⣦⡞⡜⣷⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⣀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⢠⠀⠀⠋⢰⠀⢹⠋⠙⠀⠁⠛ ⡃⣰⠎⢀⡼⠀⣀⣇⠠⠀⡟⣾⣐⢦⡑⣄⠳⣇⠀⣧⢈⡇⢻⢆⠙⠉⠉⠙⠉⠋⠖⡥⣬⢀⠀⠀⠀⠀⠀⡆⡞⠘⠀⠀⠀⠀⠃⣿⣸⠁⣼⠀⠀⠀⠋⡿⢲⠒⠒⡓⣿⣿⣯⣿⣽ ⢠⠄⢀⡜⠀⠀⠏⢰⠀⡟⢀⢸⠀⠉⡉⢣⠀⣄⠀⠀⠁⡟⣿⠾⣡⣼⢀⠋⣴⢁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠻⠈⠀⠋⣽⣿⠉⡿⢻⠓⠶⣸⢀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣼ ⠉⠁⡼⠀⠀⠇⣹⠀⠟⢠⠀⡜⠀⢳⠙⣀⢀⠀⠀⠀⡟⣾⣠⠿⣠⠀⡞⢀⠄⣀⠀⠀⠀⠀⠁⠀⠋⠚⠓⠞⠴⠤⣠⣇⣈⣷⣼⠀⠀⠀⠀⡉⡏⢚⠛⠴⠦⠭⠛⡿⣿⣿⣿⣿⢀ ⣀⣄⠀⠀⠁⠉⡉⣍⢩⠉⠉⢻⠉⠉⡉⢻⠈⠃⠋⡼⢀⠀⡞⢀⠀⠃⢸⠀⠀⠀⠀⠁⠚⡴⣤⣀⢀⠋⣠⠀⠀⠀⠀⠀⢣⠀⢤⠀⠀⠛⡿⢀⡿⠉⢾⠶⣠⠀⡏⣿⣿⣿⣿⣿⠘ ⠀⠀⠁⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⠀⠀⡄⢀⠀⠀⡀⢹⠀⠁⠋⠔⣸⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠁⠋⡖⠹⠀⠀⠀⢆⣴⣠⣀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠃⡴⢀⠀⠀⠀⠇⢠⠀⠀⠀⠁⠞⣀⠀⠀⡀⢦⠙⠈⠀⠀⠁⠀⠁⠉⠉⠛⠟⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠟⠰⠀⠁⠛⢴⣠⠀⠀⠀⠀⠀⡼⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⠤⡤⣀⠉⣞⣴⣯⣿⢿⠿⡋⣟⢿⠛ ⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠉⠉⠛⠒⠴⠤⣠⣀⣄⣤⣷⣾⢶⠴⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣴⣀⢤⡶⣶⣴⣀⠀⡆⣿⣿⣿⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⣎⣧⣠⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⣠⠀⠀⠀⠀⠀⠀⠃⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⡆⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢡⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⠂⣿⣿ ⠀⠀⠀⠀⠀⠀⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠃⣰⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣟⣿

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